Question

select the expression equal to ^3√ 108

a. 6
b. 3^3√ 3
c. 4^3√ 3
d. 3^3√ 4

Answer 1

ANSWER

3∛(4)

EXPLANATION
108 prime factorizes into 2^2 * 3^3

$\sqrt[3]{108} = \sqrt[3]{2^2 \cdot 3^3}$

Apply radical property $\sqrt[n]{ab} = \sqrt[n]{a} \cdot \sqrt[n]{b}$

   $\begin{aligned} \sqrt[3]{108} &= \sqrt[3]{2^2} \cdot \sqrt[3]{ 3^3} \\ &= \sqrt[3]{2^2} \cdot 3 \\ &= 3 \sqrt[3]{4} \end{aligned}$

Answer 2

Hi there!

Prime factors [ 108 ] = 2² × 3³

$\sqrt[3]{108}$ = $\sqrt[3]{2^{2} × 3^{3}}$

Apply radical property :-

$\sqrt[n]{ab} = \sqrt[n]{a} × \sqrt[n]{b}$

$\begin{aligned} \sqrt[3]{108} &= \sqrt[3]{2^2} × \sqrt[3]{ 3^3} \\ &= \sqrt[3]{2^2} × 3 \\ &= 3 \sqrt[3]{4} \end{aligned}$

~ Hope it helps!