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 = (625)/(10000)`

Find the prime factorization both numerator and denominator:

`(625)/(10000) = (5^4)/(2^45^4)`

The square root halves the exponents, so the number becomes

`\sqrt{(625)/(10000)} = (5^2)/(2^25^2) = (25)/(100) = 0.25`