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Pertanyaan

begin mathsize 14px style cube root of 27 cross times cube root of 125 equals... end style 

Pembahasan Soal:

Dengan menggunakkan sifat-sifat akar pangkat tiga, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 27 cross times cube root of 125 end cell equals cell cube root of 3 cubed end root cross times cube root of 5 cubed end root end cell row blank equals cell 3 cross times 5 end cell row blank equals 15 end table end style  

Sehingga, begin mathsize 14px style cube root of 27 cross times cube root of 125 equals 15 end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

K. Putri

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Terakhir diupdate 29 Maret 2021

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Pembahasan Soal:

Perkalian bentuk akar

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 1.331 end root cross times cube root of 343 end cell equals cell open parentheses 11 cubed close parentheses to the power of 1 third end exponent cross times open parentheses 7 cubed close parentheses to the power of 1 third end exponent end cell row blank equals cell 11 cross times 7 end cell row blank equals 77 end table

Jadi, cube root of 1.331 end root cross times cube root of 343 equals 77.

Roboguru

Hasil dari  adalah

Pembahasan Soal:

Diketahui cube root of a squared end root cross times a fourth root of a cubed end root memiliki akar pangkat yang berbeda sehingga untuk menentukan hasil perkaliannya maka diperlukan merebah bentuk akar menjadi bilangan berpangkat.

Jika a not equal to 0 space text dan end text space n comma m bilangan positif maka berlaku:

n-th root of a to the power of m end root equals a to the power of m over n end exponent

Maka

cube root of a squared end root cross times a fourth root of a cubed end root equals a to the power of 2 over 3 end exponent cross times a open parentheses a to the power of 3 over 4 end exponent close parentheses

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 dan a to the power of 1 equals a maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of a squared end root cross times a fourth root of a cubed end root end cell equals cell a to the power of 2 over 3 end exponent cross times a open parentheses a to the power of 3 over 4 end exponent close parentheses end cell row blank equals cell a to the power of 2 over 3 end exponent cross times a cross times a to the power of 3 over 4 end exponent end cell row blank equals cell a cross times a to the power of 2 over 3 plus 3 over 4 end exponent end cell row blank equals cell a cross times a to the power of fraction numerator 2 cross times 4 over denominator 12 end fraction plus fraction numerator 3 cross times 3 over denominator 12 end fraction end exponent end cell row blank equals cell a cross times a to the power of 8 over 12 plus 9 over 12 end exponent end cell row blank equals cell a cross times a to the power of 17 over 12 end exponent end cell row blank equals cell a cross times a to the power of 12 over 12 plus 5 over 12 end exponent end cell row blank equals cell a cross times a to the power of 12 over 12 end exponent cross times a to the power of 5 over 12 end exponent end cell row blank equals cell a cross times a to the power of 1 cross times a to the power of 5 over 12 end exponent end cell row blank equals cell a cross times a cross times a to the power of 5 over 12 end exponent end cell row blank equals cell a squared cross times a to the power of 5 over 12 end exponent end cell end table

Berdasarkan sifat bilangan berpangkat pecahan 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 cube root of a squared end root cross times a fourth root of a cubed end root end cell equals cell a squared cross times a to the power of 5 over 12 end exponent end cell row blank equals cell a squared cross times root index 12 of a to the power of 5 end root end cell row blank equals cell a squared space root index 12 of a to the power of 5 end root end cell end table

Jadi hasil dari cube root of a squared end root cross times a fourth root of a cubed end root adalah a squared space root index 12 of a to the power of 5 end root.

Oleh karena itu, jawaban yang benar adalah B.

Roboguru

Hasil dari  adalah ...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 20 plus square root of 12 cross times 3 square root of 6 end cell equals cell square root of 20 plus 3 square root of 12 cross times 6 end root end cell row blank equals cell square root of 20 plus 3 square root of 72 end cell row blank equals cell square root of 4 cross times 5 end root plus 3 square root of 36 cross times 2 end root end cell row blank equals cell 2 square root of 5 plus 3 cross times 6 square root of 2 end cell row blank equals cell 2 square root of 5 plus 18 square root of 2 end cell end table 

Jadi, square root of 20 plus square root of 12 cross times 3 square root of 6 equals 2 square root of 5 plus 18 square root of 2

Roboguru

Hasil dari  adalah..

Pembahasan Soal:

square root of 45 cross times square root of 28 equals square root of 9 cross times 5 end root cross times square root of 4 cross times 7 end root space space space space space space space space space space space space space space space space space space space equals square root of 9. square root of 5 cross times square root of 4. square root of 7 space space space space space space space space space space space space space space space space space space space equals 3 square root of 5 cross times 2 square root of 7 space space space space space space space space space space space space space space space space space space space equals space left parenthesis 3 cross times 2 right parenthesis cross times left parenthesis square root of 5 cross times square root of 7 right parenthesis space space space space space space space space space space space space space space space space space space space equals space left parenthesis 6 right parenthesis cross times left parenthesis square root of 35 right parenthesis space space space space space space space space space space space space space space space space space space space equals 6 square root of 35 

Jadi, jawaban yang tepat adalah A

Roboguru

Hasil dari adalah ....

Pembahasan Soal:

Ingat : rightwards double arrow square root of a cross times square root of b equals square root of a cross times b end root rightwards double arrow a square root of b plus-or-minus c square root of b equals open parentheses a plus-or-minus c close parentheses square root of b

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 24 open parentheses square root of 8 minus 2 square root of 3 close parentheses plus fraction numerator 24 over denominator square root of 2 end fraction end cell equals cell square root of 192 minus 2 square root of 72 plus fraction numerator 24 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell square root of 64 cross times 3 end root minus 2 square root of 36 cross times 2 end root plus 24 over 2 square root of 2 end cell row blank equals cell 8 square root of 3 minus 12 square root of 2 plus 12 square root of 2 end cell row blank equals cell 8 square root of 3 end cell end table

Jadi, jawaban yang tepat adalah D.

Roboguru

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