# What is 625^(1/4) ?

Jul 12, 2017

${625}^{\frac{1}{4}} = 5$

#### 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:

$625 = 5 \cdot 125 = 5 \cdot 5 \cdot 25 = 5 \cdot 5 \cdot 5 \cdot 5 = {5}^{4}$

Hence:

${625}^{\frac{1}{4}} = {\left({5}^{4}\right)}^{\frac{1}{4}} = {5}^{4 \cdot \frac{1}{4}} = {5}^{1} = 5$