Iklan

Iklan

Pertanyaan

Tentukan hasil operasi bilanganberikut! d. 3 ​ ( 2 6 ​ − 25 ​ ) e. ( 6 ​ + 8 ​ ) ( 6 ​ − 3 ​ ) f. ( 2 3 ​ − 6 ​ ) ( 8 ​ − 2 ​ ) g. ( 3 5 ​ − 6 ​ ) ( 3 5 ​ + 6 ​ )

Tentukan hasil operasi bilangan berikut!
d. 
e. 
f. 
g. 

Iklan

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

hasil dari adalah .

hasil dari open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses adalah 39.

Iklan

Pembahasan

Ingat sifat distributif perkalian sebagai berikut. Sehingga d. diperoleh sebagai berikut. Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu maka Jika dapat difaktorkan menjadi dengan bilangan berpangkat maka dapat disederhanakan sehingga Jadi hasil dari adalah . e. Diperoleh sebagai berikut. Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu maka Jika dapat difaktorkan menjadi dengan bilangan berpangkat maka dapat disederhanakan sehingga diperoleh Bentuk akar dengan akar dan bilangan pokok sama dapat dikurangkan dengan menggunakan sifat distributif sebagai berikut Sehingga Jadi hasil dari adalah . f. diperoleh sebagai berikut. Berdasarkan perkalian bentuk akar dengan akar pangkat sama yaitu maka Jika dapat difaktorkan menjadi dengan bilangan berpangkat maka dapat disederhanakan sehingga diperoleh Bentuk akar dengan akar dan bilangan pokok sama dapat dikurangkan dengan menggunakan sifat distributif sebagai berikut Sehingga Jadi hasil dari adalah . g. Ingat rumus perkalian suku dua bentuk aljabaryaitu Sehingga diperoleh sebagai berikut. Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu sehingga Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat dan maka Jadi hasil dari adalah .

Ingat sifat distributif perkalian sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a open parentheses b plus c close parentheses end cell equals cell a b plus b c end cell row cell open parentheses a plus b close parentheses open parentheses c plus d close parentheses end cell equals cell a c plus a d plus b c plus b d end cell end table

Sehingga

d. square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses end cell equals cell square root of 3 cross times 2 square root of 6 minus square root of 3 cross times square root of 25 end cell row blank equals cell square root of 3 cross times 2 square root of 6 minus square root of 3 cross times 5 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 comma a not equal to 0 space text dan end text space b not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses end cell equals cell square root of 3 cross times 2 square root of 6 minus square root of 3 cross times square root of 25 end cell row blank equals cell square root of 3 cross times 2 square root of 6 minus square root of 3 cross times 5 end cell row blank equals cell 2 square root of 3 cross times 6 end root minus 5 square root of 3 end cell row blank equals cell 2 square root of 18 minus 5 square root of 3 end cell row blank blank blank end table

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses end cell equals cell 2 square root of 3 cross times 6 end root minus 5 square root of 3 end cell row blank equals cell 2 square root of 18 minus 5 square root of 3 end cell row blank equals cell 2 square root of 9 cross times 2 end root minus 5 square root of 3 end cell row blank equals cell 2 square root of 3 squared cross times 2 end root minus 5 square root of 3 end cell row blank equals cell 2 cross times 3 square root of 2 minus 5 square root of 3 end cell row blank equals cell 6 square root of 2 minus 5 square root of 3 end cell end table

Jadi hasil dari square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 square root of 2 minus 5 square root of 3 end cell end table.

e. open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses Diperoleh sebagai berikut.

begin mathsize 12px style open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses equals square root of 6 cross times square root of 6 minus square root of 6 cross times square root of 3 plus square root of 8 cross times square root of 6 minus square root of 8 cross times square root of 3 end style

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

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses end cell equals cell square root of 6 cross times square root of 6 minus square root of 6 cross times square root of 3 plus square root of 8 cross times square root of 6 minus square root of 8 cross times square root of 3 end cell row blank equals cell square root of 6 cross times 6 end root minus square root of 6 cross times 3 end root plus square root of 8 cross times 6 end root minus square root of 8 cross times 3 end root end cell row blank equals cell square root of 36 minus square root of 18 plus square root of 48 minus square root of 24 end cell end table end style

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses end cell equals cell square root of 6 cross times 6 end root minus square root of 6 cross times 3 end root plus square root of 8 cross times 6 end root minus square root of 8 cross times 3 end root end cell row blank equals cell square root of 36 minus square root of 18 plus square root of 48 minus square root of 24 end cell row blank equals cell 6 minus square root of 9 cross times 2 end root plus square root of 16 cross times 3 end root minus square root of 4 cross times 6 end root end cell row blank equals cell 6 minus square root of 3 squared cross times 3 end root plus square root of 4 squared cross times 3 end root minus square root of 2 squared cross times 6 end root end cell row blank equals cell 6 minus 3 square root of 3 plus 4 square root of 3 minus 2 square root of 6 end cell end table

Bentuk akar dengan akar dan bilangan pokok sama dapat dikurangkan dengan menggunakan sifat distributif sebagai berikut

a n-th root of b minus c n-th root of b equals open parentheses a minus c close parentheses n-th root of b

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses end cell equals cell square root of 6 cross times 6 end root minus square root of 6 cross times 3 end root plus square root of 8 cross times 6 end root minus square root of 8 cross times 3 end root end cell row blank equals cell square root of 36 minus square root of 18 plus square root of 48 minus square root of 24 end cell row blank equals cell 6 minus square root of 9 cross times 2 end root plus square root of 16 cross times 3 end root minus square root of 4 cross times 6 end root end cell row blank equals cell 6 minus square root of 3 squared cross times 3 end root plus square root of 4 squared cross times 3 end root minus square root of 2 squared cross times 6 end root end cell row blank equals cell 6 minus 3 square root of 3 plus 4 square root of 3 minus 2 square root of 6 end cell row blank equals cell 6 minus square root of 3 open parentheses 3 minus 4 close parentheses minus 2 square root of 6 end cell row blank equals cell 6 minus open parentheses negative 1 close parentheses square root of 3 minus 2 square root of 6 end cell row blank equals cell 6 plus square root of 3 minus 2 square root of 6 end cell row blank blank blank end table

Jadi hasil dari open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 plus square root of 3 minus 2 square root of 6 end cell row blank blank blank end table.

f. open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses diperoleh sebagai berikut.

begin mathsize 12px style open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses equals 2 square root of 3 cross times square root of 8 minus 2 square root of 3 cross times square root of 2 minus square root of 6 cross times square root of 8 plus square root of 6 cross times square root of 2 end style

Berdasarkan 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

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses end cell equals cell 2 square root of 3 cross times square root of 8 minus 2 square root of 3 cross times square root of 2 minus square root of 6 cross times square root of 8 plus square root of 6 cross times square root of 2 end cell row blank equals cell 2 square root of 3 cross times 8 end root minus 2 square root of 3 cross times 2 end root minus square root of 6 cross times 8 end root plus square root of 6 cross times 2 end root end cell row blank equals cell 2 square root of 24 minus 2 square root of 6 minus square root of 48 plus square root of 12 end cell row blank blank blank end table end style

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses end cell equals cell 2 square root of 3 cross times 8 end root minus 2 square root of 3 cross times 2 end root minus square root of 6 cross times 8 end root plus square root of 6 cross times 2 end root end cell row blank equals cell 2 square root of 24 minus 2 square root of 6 minus square root of 48 plus square root of 12 end cell row blank equals cell 2 square root of 4 cross times 6 end root minus 2 square root of 6 minus square root of 16 cross times 3 end root plus square root of 4 cross times 3 end root end cell row blank equals cell 2 square root of 2 squared cross times 6 end root minus 2 square root of 6 minus square root of 4 squared cross times 3 end root plus square root of 2 squared cross times 3 end root end cell row blank equals cell 2 cross times 2 square root of 6 minus 2 square root of 6 minus 4 square root of 3 plus 2 square root of 3 end cell row blank equals cell 4 square root of 6 minus 2 square root of 6 minus 4 square root of 3 plus 2 square root of 3 end cell end table

Bentuk akar dengan akar dan bilangan pokok sama dapat dikurangkan dengan menggunakan sifat distributif sebagai berikut

a n-th root of b minus c n-th root of b equals open parentheses a minus c close parentheses n-th root of b

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses end cell equals cell 4 square root of 6 minus 2 square root of 6 minus 4 square root of 3 plus 2 square root of 3 end cell row blank equals cell open parentheses 4 minus 2 close parentheses square root of 6 minus open parentheses 4 minus 2 close parentheses square root of 3 end cell row blank equals cell 2 square root of 6 minus 2 square root of 3 end cell end table

Jadi hasil dari open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 square root of 6 minus 2 square root of 3 end cell end table.

g. Ingat rumus perkalian suku dua bentuk aljabar yaitu

open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared

Sehingga open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses diperoleh sebagai berikut.

open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses equals open parentheses 3 square root of 5 close parentheses squared minus open parentheses square root of 6 close parentheses squared

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 space a not equal to 0 sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses end cell equals cell open parentheses 3 square root of 5 close parentheses squared minus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 3 cross times 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat 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 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses end cell equals cell open parentheses 3 square root of 5 close parentheses squared minus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 3 cross times 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 3 squared cross times open parentheses 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared 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 dan a to the power of 1 equals a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses end cell equals cell open parentheses 3 square root of 5 close parentheses squared minus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 3 cross times 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 3 squared cross times open parentheses 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 9 cross times 5 to the power of 1 half cross times 2 end exponent minus 6 to the power of 1 half cross times 2 end exponent end cell row blank equals cell 9 cross times 5 to the power of 1 minus 6 to the power of 1 end cell row blank equals cell 9 cross times 5 minus 6 end cell row blank equals cell 45 minus 6 end cell row blank equals 39 end table

Jadi hasil dari open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses adalah 39.

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

288

Muhammad irmansyah Alvata Alvata

Jawaban tidak sesuai

Iklan

Iklan

Pertanyaan serupa

Tentukan hasil operasi bilanganberikut! a. ( 6 ​ + 6 ) 2 b. ( 3 3 ​ − 5 ​ ) 2 c. ( 3 x 2 ​ − 4 ) 2

3

4.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

[email protected]

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia