Question

When 400^(1/4) is simplified, the result is msqrtn where m and n are positive integers and n is as small as possible. What is m+n?

Answer 1

7

Explanation:

400^(1/4) = m*sqrt(n)

(20^2)^(1/4) = m*sqrt(n)

20^(2*(1/4)) = m*sqrt(n)

20^(1/2) = m*sqrt(n)

sqrt(20) = m*sqrt(n)

2*sqrt(5) = m*sqrt(n)

m = 2, n = 5

m + n = 2 + 5 = 7