Pertanyaan

3 2 3 + 5 27 72 − 54 = ...

$3 \frac{3}{2} + 5 \frac{72}{27} - 54 = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai

3 square root of 3 over 2 end root plus 5 square root of 72 over 27 end root minus square root of 54

adalah

Pembahasan

Ingat aturan bentuk akar berikut, Maka, Jadi, nilai adalah .

Ingat aturan bentuk akar berikut,

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

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 square root of 3 over 2 end root plus 5 square root of 72 over 27 end root minus square root of 54 end cell equals cell 3 square root of fraction numerator 3 cross times 2 over denominator 2 cross times 2 end fraction end root plus 5 square root of fraction numerator 72 divided by 3 over denominator 27 divided by 3 end fraction end root minus square root of 54 end cell row blank equals cell 3 square root of 6 over 4 end root plus 5 square root of 24 over 9 end root minus square root of 9 cross times 6 end root end cell row blank equals cell 3 square root of 1 fourth cross times 6 end root plus 5 square root of 4 over 9 cross times 6 end root minus square root of 9 cross times 6 end root end cell row blank equals cell 3 square root of 1 over 2 squared cross times 6 end root plus 5 square root of 2 squared over 3 squared cross times 6 end root minus square root of 3 squared cross times 6 end root end cell row blank equals cell 3 open parentheses 1 half close parentheses square root of 6 plus 5 open parentheses 2 over 3 close parentheses square root of 6 minus 3 square root of 6 end cell row blank equals cell 3 over 2 square root of 6 plus 10 over 3 square root of 6 minus 3 square root of 6 end cell row blank equals cell open parentheses 3 over 2 plus 10 over 3 minus 3 close parentheses square root of 6 end cell row blank equals cell open parentheses fraction numerator 3 open parentheses 3 close parentheses over denominator 2 open parentheses 3 close parentheses end fraction plus fraction numerator 10 open parentheses 2 close parentheses over denominator 3 open parentheses 2 close parentheses end fraction minus fraction numerator 3 cross times 6 over denominator 6 end fraction close parentheses square root of 6 end cell row blank equals cell open parentheses 9 over 6 plus 20 over 6 minus 18 over 6 close parentheses square root of 6 end cell row blank equals cell open parentheses fraction numerator 29 minus 18 over denominator 6 end fraction close parentheses square root of 6 end cell row blank equals cell 11 over 6 square root of 6 end cell row blank blank blank end table$

Jadi, nilai 3 square root of 3 over 2 end root plus 5 square root of 72 over 27 end root minus square root of 54 adalah 11 over 6 square root of 6 .