How do you find the square root of 5 to the 4th power?

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Answer 1 · 2015-09-14T19:59:05

It is $sqrt(5^4)=5^2=25$

Answer 2 · 2015-09-14T20:07:59

The question is slightly ambiguous, but both $(sqrt(5))^4$ and $sqrt(5^4)$ are equal to $25$

$(a^b)^c = a^(bc)$ for $a, b, c >= 0$

So:
$(sqrt(5))^4 = ((sqrt(5))^2)^2 = 5^2 = 25$

Also:
$sqrt(5^4) = sqrt((5^2)^2) = 5^2 = 25$

Alternatively using fractional exponents:

$sqrt(a) = a^(1/2)$

So:
$(sqrt(5))^4 = (5^(1/2))^4 = 5^(1/2 * 4) = 5^2 = 25$

and:
$sqrt(5^4) = (5^4)^(1/2) = 5^(4*1/2) = 5^2 = 25$