Question

What are the real square roots of .0625

Answer 1

Assuming you can't simply put the number inside a calculator: write the number as a fraction:

$0.0625 = \frac{625}{10000}$

Find the prime factorization both numerator and denominator:

$\frac{625}{10000} = \frac{5^4}{2^45^4}$

The square root halves the exponents, so the number becomes

$\sqrt{\frac{625}{10000}} = \frac{5^2}{2^25^2} = \frac{25}{100} = 0.25$