Question

What is the cube root of 27a^12

Answer 1

Cube root of 27 a^12 will be:  3 a^4.

Answer 2

Answer:

Cube-root defines: A number is a special value that, when used in a multiplication three times, gives that number.

Its symbol is denoted by: $\sqrt[3]{}$

USing Law of radical:

1. $\sqrt[n]{ab}= \sqrt[n]{a} \cdot \sqrt[n]{b}$

2. $\sqrt[n]{x^n} =(\sqrt[n]{x} )^n =\sqrt[n]{x^n} =x$

To find the cube root of $27a^{12}$ ;

By the definition of cube root

$\sqrt[3]{27 a^{12}}$ = $\sqrt[3]{27} \cdot \sqrt[3]{a^{12}}$ [Using [1]]

we can write 27 as $3 \times 3 \times 3 = 3^3$ and $a^{12} = (a^4)^3$

then;

$\sqrt[3]{27 a^{12}}$ = $\sqrt[3]{3^3} \cdot \sqrt[3]{a^{4}^3}$

 = $3 \cdot a^4$       [ Using [2] ]

therefore, the cube root of $27a^{12}$ is $3a^4$