# What is the simplest radical form of sqrt160?

Aug 5, 2016

$4 \sqrt{10}$

#### Explanation:

Write 160 as the product of its prime factors, then we know what we are dealing with.

$\sqrt{160} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5} = \sqrt{{2}^{5} \times 5}$

=$\sqrt{{2}^{5} \times 5} = \sqrt{{2}^{4} \times 2 \times 5}$

=$4 \sqrt{10}$

Aug 5, 2016

Radicals can be split by multiplication. It helps to be able to find perfect squares underneath the radicals during the factorization, and $16$ is a convenient perfect square.

If it helps, try going in steps of factoring out $2$.

$\sqrt{160}$

$\sqrt{2 \cdot 80}$

$\sqrt{2 \cdot 2 \cdot 40}$

$\sqrt{2 \cdot 2 \cdot 2 \cdot 20}$

$\sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 10}$

$= \sqrt{16 \cdot 10}$

$= \sqrt{16} \cdot \sqrt{10}$

Since $\sqrt{16} = 4$, we end up with $\textcolor{b l u e}{4 \sqrt{10}}$.