Question

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$\sqrt{4 \sqrt{4 \sqrt{4 \sqrt{4 \sqrt{4 = } } } } }$
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Answer 1

Step-by-step explanation:

Formula for solving this type of questions

$x {}^{ \frac{2 {}^{n} - 1}{2 {}^{n} } }$

where

x = the number in the root

and

n = number of times x repeated

So, here

x = 4 and n= 5

After substituting value

The answer will be

$4 {}^{ \frac{2 {}^{5} - 1}{2 {}^{5} } } \\ = 4 {}^{ \frac{32 - 1}{32} } \\ = 4 {}^{ \frac{31}{32} }$

So

$\sqrt{4 \sqrt{4 \sqrt{4 \sqrt{4 \sqrt{4} } } } } = 4 {}^{ \frac{31}{32} }$