The correct option is A 4 Given, x^√(x)=√(x^x) or, #160; x^√(x)=x^x2 or, √(x)=x2 Squaring both sides we get, x=x^24 Since x 0 so ...

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Finding Square Root through Prime Factorisation

Solve: x√x=√...

Question

Solve:
$x^{\sqrt{x}} = \sqrt{x^{x}}$ .

2

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3

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4

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none of these

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Solution

The correct option is A $4$
Given,
$x^{\sqrt{x}} = \sqrt{x^{x}}$
or, $x^{\sqrt{x}} = x^{\frac{x}{2}}$
or, $\sqrt{x} = \frac{x}{2}$
Squaring both sides we get,
$x = \frac{x^{2}}{4}$
Since $x \neq 0$ so $x = 4$ .

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