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

1 Answer
May 1, 2017

#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)#