Question

Which expression is equivalent to √4j^4/9k^8?

Answer 1

$\frac{ 2j^{2} }{ 3^{4} }$
SQRT each individual bit: 4 and$j^{4}$ and 9 and $k^{8}$

Answer 2

Answer:

Option (4) is correct.

An equivalent expression to the given expression   $\sqrt{\frac{4j^4}{9k^8}}$ is $\frac{2j^2}{3k^4}$

Step-by-step explanation:

Given expression  $\sqrt{\frac{4j^4}{9k^8}}$

We have to choose an equivalent expression to the given expression   $\sqrt{\frac{4j^4}{9k^8}}$

Consider the given expression  $\sqrt{\frac{4j^4}{9k^8}}$

Apply radical rule,

$\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$=\frac{\sqrt{4}\sqrt{j^4}}{\sqrt{9}\sqrt{k^8}}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:$

$\sqrt{4j^4}=\sqrt{4}\sqrt{j^4}$

$\sqrt{9k^8}=\sqrt{9}\sqrt{k^8}$

We have,

$=\frac{\sqrt{4}\sqrt{j^4}}{\sqrt{9}\sqrt{k^8}}$

$=\frac{2\sqrt{j^4}}{3\sqrt{k^8}}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}}$

$=\frac{2j^2}{3k^4}$

Thus, An equivalent expression to the given expression   $\sqrt{\frac{4j^4}{9k^8}}$ is $\frac{2j^2}{3k^4}$