Question

Prove that square root of x is equal to x1/2

Answer 1

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Here is your answer...✌

To prove :

$\sqrt{x} = {x}^{ \frac{1}{2} }$

Proof :

Let

$\sqrt{x} = {x}^{k}$
Squaring both sides we get,

${ ( \sqrt{x} )}^{2} = { ({x}^{ k} )}^{2} \\ \\ \implies x = {x}^{2k} \\ \\ \implies {x}^{1} = {x}^{2k}$

On equating the power of x , We get

$2k = 1 \: \implies k = \frac{1}{2}$
Hence,

$\sqrt{x} = {x}^{ \frac{1}{2} } \: \: \: \: \: \: \: \: | \: proved \: |$