Question

What is `625^(1/4)` ?

Answer 1

`625^(1/4) = 5`

Explanation:

First find the prime factorisation of `625`:

• `625` is not divisible by `2` since it ends with an odd digit.

• `625` is not divisible by `3` since the sum of its digits is not divisible by `3`. That is: `6+2+5 = 13` which is not divisible by `3`.

• `625` is divisible by `5` since it ends with a `5` and we find:

`625 = 5*125 = 5*5*25 = 5*5*5*5 = 5^4`

Hence:

`625^(1/4) = (5^4)^(1/4) = 5^(4*1/4) = 5^1 = 5`