Question

What is `625^(1/8)` in radical form?

Answer 1

`root(8)(625) = sqrt(5)`

Explanation:

Use the exponent rules `sqrt(x) = x^(1/2)`; `" "root(3)(y) = y^(1/3)`

and the exponent power rule `(x^m)^n = x^(m*n)`

`625^(1/8) = root(8)(625)`

Simplified: `625^(1/8) = (625^(1/2))^(1/4) = ((625^(1/2))^(1/2))^(1/2)`

`625^(1/8) = sqrt(sqrt(sqrt(625))) = sqrt(sqrt(25)) = sqrt(5)`