Roboguru

Pertanyaan

begin mathsize 14px style cube root of 2 cross times cube root of 6 cross times cube root of 18 equals... end style 

  1. begin mathsize 14px style 3 end style 

  2. size 14px 4 

  3. size 14px 6 

  4. size 14px 12 

Pembahasan Video:

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell cube root of 2 cross times cube root of 6 cross times cube root of 18 end cell equals cell cube root of 2 cross times 6 cross times 18 end root end cell row blank equals cell cube root of 2 cross times 6 cross times left parenthesis 6 cross times 3 right parenthesis end root end cell row blank equals cell cube root of left parenthesis 2 cross times 3 right parenthesis cross times 6 cross times 6 end root end cell row blank equals cell cube root of 6 cubed end root end cell row blank equals 6 end table end style

Jadi, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 13 September 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Tentukan nilai dari

Pembahasan Soal:

Perkalian bentuk akar dengan akar pangkat sama

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 8 cross times square root of 4 end cell equals cell square root of 8 cross times 4 end root end cell row blank equals cell square root of 32 end cell row blank equals cell square root of 16 cross times 2 end root end cell row blank equals cell square root of 16 cross times square root of 2 end cell row blank equals cell 4 square root of 2 end cell end table

Jadi, square root of 8 cross times square root of 4 equals 4 square root of 2.

0

Roboguru

Pembahasan Soal:

Perhatikan sifat-sifat bentuk bilangan berpangkat dan hubungannya dengan bilangan bentuk akar.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of cube root of 16 end root cross times cube root of 1 fourth end root end cell equals cell square root of cube root of 4 squared end root end root cross times cube root of 4 to the power of negative 1 end exponent end root end cell row blank equals cell square root of 4 to the power of 2 over 3 end exponent end root cross times 4 to the power of negative 1 third end exponent end cell row blank equals cell open parentheses 4 to the power of 2 over 3 end exponent close parentheses to the power of 1 half end exponent cross times 4 to the power of negative 1 third end exponent end cell row blank equals cell 4 to the power of 2 over 6 end exponent cross times 4 to the power of negative 1 third end exponent end cell row blank equals cell 4 to the power of 2 over 6 minus 1 third end exponent end cell row blank equals cell 4 to the power of 0 end cell row blank equals 1 end table end style

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Tentukan hasil pemangkatan akar-akar bilangan berikut! l.

Pembahasan Soal:

Ingat kembali rumus berikut.

  • square root of a squared cross times b end root equals a square root of b
  • square root of a cross times square root of b equals square root of a cross times b end root 
  • open parentheses square root of a plus square root of b close parentheses squared equals open parentheses square root of a close parentheses squared plus 2 open parentheses square root of a close parentheses open parentheses square root of b close parentheses plus open parentheses square root of b close parentheses squared 

Dari rumus di atas, diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 7 square root of 2 a end root plus square root of 8 b end root close parentheses squared end cell equals cell 7 squared open parentheses square root of 2 a end root close parentheses squared plus 2 open parentheses 7 square root of 2 a end root close parentheses open parentheses square root of 8 b end root close parentheses plus open parentheses square root of 8 b end root close parentheses squared end cell row blank equals cell 49 cross times 2 a plus 14 square root of 2 a cross times 8 b end root plus 8 b end cell row blank equals cell 98 a plus 14 square root of 16 a b end root plus 8 b end cell row blank equals cell 98 a plus 8 b plus 14 square root of 4 squared cross times a b end root end cell row blank equals cell 98 a plus 8 b plus 14 cross times 4 square root of a b end root end cell row blank equals cell 98 a plus 8 b plus 56 square root of a b end root end cell end table 

Jadi, hasil dari open parentheses 7 square root of 2 a end root plus square root of 8 b end root close parentheses squared adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 98 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 56 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of a b end root end cell end table.

0

Roboguru

Tentukan hasil operasi bilangan berikut dalam bentuk akar! d.  e.  f.

Pembahasan Soal:

d. Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma a not equal to 0 maka open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed diperoleh sebagai berikut.

open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed equals open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses 4 a close parentheses to the power of 1 half cross times 3 end exponent cross times open parentheses 3 a close parentheses to the power of 3 over 4 cross times 3 end exponent end cell row blank equals cell open parentheses 4 a close parentheses to the power of 3 over 2 end exponent cross times open parentheses 3 a close parentheses to the power of 9 over 4 end exponent end cell end table

Berdasarkan sifat bilangan berpangkat a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses 4 a close parentheses to the power of 1 half cross times 3 end exponent cross times open parentheses 3 a close parentheses to the power of 3 over 4 cross times 3 end exponent end cell row blank equals cell open parentheses 4 a close parentheses to the power of 3 over 2 end exponent cross times open parentheses 3 a close parentheses to the power of 9 over 4 end exponent end cell row blank equals cell 4 to the power of 3 over 2 end exponent cross times a to the power of 3 over 2 end exponent cross times 3 to the power of 9 over 4 end exponent cross times a to the power of 9 over 4 end exponent end cell row blank equals cell open parentheses 2 squared close parentheses to the power of 3 over 2 end exponent cross times a to the power of 3 over 2 plus 9 over 4 end exponent cross times 3 to the power of fraction numerator 8 plus 1 over denominator 4 end fraction end exponent end cell row blank equals cell 2 to the power of 2 cross times 3 over 2 end exponent cross times a to the power of fraction numerator 3 cross times 2 plus 9 over denominator 4 end fraction end exponent cross times 3 to the power of 8 over 4 plus 1 fourth end exponent end cell row blank equals cell 2 cubed cross times a to the power of fraction numerator 6 plus 9 over denominator 4 end fraction end exponent cross times 3 to the power of 2 plus 1 fourth end exponent end cell row blank equals cell 8 cross times a to the power of 15 over 4 end exponent cross times 3 squared cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 8 cross times 9 cross times a to the power of fraction numerator 12 plus 3 over denominator 4 end fraction end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a to the power of 12 over 4 plus 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank blank blank end table

Berdasarkan sifat bilangan berpangkat pecahan yaitu a to the power of m over n end exponent equals n-th root of a to the power of m end root comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times fourth root of a cubed end root cross times fourth root of 3 to the power of 1 end root end cell row blank equals cell 72 a cubed cross times fourth root of a cubed end root cross times fourth root of 3 end cell row blank blank blank end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times fourth root of a cubed end root cross times fourth root of 3 to the power of 1 end root end cell row blank equals cell 72 a cubed cross times fourth root of a cubed end root cross times fourth root of 3 end cell row blank equals cell 72 a cubed cross times fourth root of a cubed cross times 3 end root end cell row blank equals cell 72 a cubed fourth root of 3 a cubed end root end cell row blank blank blank end table

Jadi hasil dari open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed dalam bentuk akar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 72 a cubed fourth root of 3 a cubed end root end cell row blank blank blank end table.

e. Berdasarkan aturan pembagian bentuk akar dengan akar pangkat sama yaitu fraction numerator n-th root of a over denominator n-th root of b end fraction equals n-th root of a over b end root maka open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell end table

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell row blank equals cell 4 cubed cross times open parentheses cube root of 1 half end root close parentheses cubed end cell end table

Ingat bahwa n-th root of a to the power of m end root equals open parentheses n-th root of a close parentheses to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell row blank equals cell 4 cubed cross times open parentheses cube root of 1 half end root close parentheses cubed end cell row blank equals cell 64 cross times cube root of open parentheses 1 half close parentheses cubed end root end cell row blank equals cell 64 cross times 1 half end cell row blank equals 32 end table

Jadi hasil dari open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed adalah 32.

f. Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma a not equal to 0 maka open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 diperoleh sebagai berikut.

open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 equals open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent close parentheses to the power of 4 cross times 3 to the power of 4 cross times open parentheses b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent close parentheses to the power of 4 cross times 3 to the power of 4 cross times open parentheses b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses 8 b squared close parentheses to the power of 1 third cross times 4 end exponent cross times 81 cross times b to the power of 3 over 2 cross times 4 end exponent end cell row blank equals cell open parentheses 8 b squared close parentheses to the power of 3 over 4 end exponent cross times 81 cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 cross times 3 over 4 end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 3 over 2 end exponent cross times b to the power of 6 end cell end table

Berdasarkan bilangan berpangkat a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 3 over 2 end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of fraction numerator 2 plus 1 over denominator 2 end fraction end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 over 2 plus 1 half end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 1 cross times b to the power of 1 half end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 1 plus 6 end exponent cross times b to the power of 1 half end exponent end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 7 cross times b to the power of 1 half end exponent end cell end table

Berdasarkan sifat bilangan berpangkat pecahan yaitu a to the power of m over n end exponent equals n-th root of a to the power of m end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 7 cross times b to the power of 1 half end exponent end cell row blank equals cell 81 b to the power of 7 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of fraction numerator 1 cross times 2 over denominator 2 cross times 2 end fraction end exponent end cell row blank equals cell 81 b to the power of 7 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 over 4 end exponent end cell row blank equals cell 81 b to the power of 7 fourth root of 8 cubed b squared end root end cell end table

Jadi hasil dari open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 81 b to the power of 7 fourth root of 8 cubed b squared end root. end cell end table

 

0

Roboguru

adalah belah ketupat dengan panjang  cm dan  cm. Hitunglah: b. Keliling belah ketupat

Pembahasan Soal:

 

Ingat kembali rumus berikut.

  • Menentukan panjang sisi miring pada segitiga dengan menggunakan teorema pythagoras c equals square root of a squared plus b squared end root
  • Belah ketupat memiliki empat sisi yang sama panjang
  • Keliling space belah space ketupat space A B C D space equals 4 cross times s  

Dari rumus di atas, deiperoleh perhitungan sebagai berikut.

Perhatikan gambar berikut.

Diketahui segitiga OAB merupakan segitiga siku-siku di O, dengan panjang A O equals 4 square root of 6 cm dan B O equals 4 square root of 3 cm. 

Akan di tentukan panjang AB (sisi miring pada segitiga OAB)

table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals cell square root of A O squared plus B O squared end root end cell row blank equals cell square root of open parentheses 4 square root of 6 close parentheses squared plus open parentheses 4 square root of 3 close parentheses squared end root end cell row blank equals cell square root of 16 cross times 6 plus 16 cross times 3 end root end cell row blank equals cell square root of 96 plus 48 end root end cell row blank equals cell square root of 144 end cell row blank equals cell square root of 12 squared end root end cell row blank equals cell 12 space cm end cell end table 

Dengan demikian panjang sisi pada belah ketupat adalah 12 cm.

Maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell Keliling space belah space ketupat space A B C D space end cell equals cell 4 cross times s end cell row blank equals cell 4 cross times 12 end cell row blank equals cell 48 space cm end cell end table  

Jadi, keliling belah ketupat A B C D adalah 48 cm.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved