\(\sqrt{4}^{1/2}\) = ?

Concept Used:-

Any exponent or power of a number is half (1/2) is nothing but the square root of that number.

\(\Rightarrow x^{1/2}= \sqrt {x}\)

Also, the square of a number can cancel out its square root.

\(\Rightarrow \sqrt{x^{2}}= x\)

Explanation:-

Given term is \(\sqrt{4}^{1/2}\). Here in this term the power of 4 is half and there is a root applied over it. Thus, from the above definition it can be simplified as,

\(\Rightarrow \sqrt{4}^{1/2}= \sqrt{\sqrt{4}}\\ \Rightarrow \sqrt{4}^{1/2}= \sqrt{\sqrt{2\times2}}\\ \Rightarrow \sqrt{4}^{1/2}= \sqrt{\sqrt{2^2}}\\ \Rightarrow \sqrt{4}^{1/2}= \sqrt{2}\)

So, the simplified value of the given number is √2.

Hence, the correct option is 3.