# What is (25 xx 5)^(1/3)?

${\left(5 \times 5 \times 5\right)}^{\frac{1}{3}} = 5$

#### Explanation:

${\left(25 \times 5\right)}^{\frac{1}{3}}$

We can rewrite this as:

${\left(5 \times 5 \times 5\right)}^{\frac{1}{3}}$

Remember that just as with, say $\sqrt{4} = {4}^{\frac{1}{2}} = {\left(2 \times 2\right)}^{\frac{1}{2}} = 2$, we can do the same thing here with the cube root:

${\left(5 \times 5 \times 5\right)}^{\frac{1}{3}} = 5$

Mar 29, 2017

$5$

#### Explanation:

Expression $= {\left(25 \times 5\right)}^{\frac{1}{3}} = \sqrt[3]{125}$

In solving roots of integers it is often useful to express the integer as the product of its prime factors.

Here: $125 = 5 \times 5 \times 5$

So: $\sqrt[3]{125} = \sqrt[3]{5 \times 5 \times 5}$

Since $5$ occurs three times we may take it through the root sign.

Hence: $\sqrt[3]{125} = 5$