Question

If $\sqrt{5^n}=125$ then find the value of $5^{\sqrt[n]{n64}}$.

• A. 25
• B. 15
• C. 30
• D. 6

Answer 1

The correct option is A 25

Given $\sqrt{5^n}=125$
$\Rightarrow 5^{\frac{n}{2}}=5\times 5\times 5=5^3$
$\Rightarrow n=6$
$\therefore 5^{\sqrt[n]{n64}}=5^2$ ($\because 6^{th}$ root of 64 = 2)
$=25$