Question

What is the radical form of each of the given expressions?

Answer 1

ANSWER

The radical form of the expression
${a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} }$
Note that
$n = 2 \: or \: m = 1$
are not written explicitly. However, greater values are written explicitly.

So, for ${2}^{ \frac{1}{2} }$

$n=2, m=1$



This implies that, we will just write
${2}^{ \frac{1}{2} } = \sqrt{2}$



for ${2}^{ \frac{2}{3} }$

$n=3, m=2$

This implies that,

${2}^{ \frac{2}{3} } = \sqrt[3]{ {2}^{2} }$


Similarly,

${3}^{ \frac{3}{2} } = \sqrt{ {3}^{3} }$

${3}^{ \frac{1}{3} } = \sqrt[3]{ {3}}$

Answer 2

2^1/2     =           √2
2^2/3     =           ∛2^2
3^3/2     =            √3^3
3^1/3     =            ∛3

hope it helps