Question

$\sqrt[x]{a} = k$ then $\sqrt[2x]{x^{2} } = ?$


Options:

a) k²

b) $\frac{1}{k}$

c) 2k

d) k

Answer 1

b) 1/k

Step-by-step explanation:

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Answer 2

Given :    $\sqrt[x]{a} =k$

To find :  $\sqrt[2x]{a^2}$    correction in question data

a) k²

b) $\frac{1}{k}$

c) 2k

d) k

Solution:

$\sqrt[n]{x} =x^{\frac{1}{n} }$

xᵃᵇ = (xᵃ)ᵇ = (xᵇ)ᵃ

$\sqrt[x]{a} =k\\\implies a^{\frac{1}{x} }=k$

$\sqrt[2x]{a^2}\\= (a^2)^{\frac{1}{2x} }\\= (a)^{\frac{2}{2x} }\\= (a)^{\frac{1}{x} }\\= k$

Hence   $\sqrt[2x]{a^2}$  = k  

Correct option is d) k

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