# How do you simplify sqrt(1,440)?

Mar 9, 2018

$12 \sqrt{10}$

#### Explanation:

$\text{note that " 1440=144xx10" and 144 is a perfect square}$

$\text{using the "color(blue)"law of radicals}$

•color(white)(x)sqrt(ab)=sqrtaxxsqrtb

$\Rightarrow \sqrt{1440} = \sqrt{144 \times 10}$

$\textcolor{w h i t e}{\times \times \times x} = \sqrt{144} \times \sqrt{10} = 12 \sqrt{10}$

Mar 9, 2018

$12 \sqrt{10}$

#### Explanation:

When you are simplifying radicals, you need to find two numbers. Between those two numbers, one HAS to be a perfect square, or it does not simplify.

Here, we are given:

$\sqrt{1440}$

We can see here that there is an easy and more noticeable factorization:

$\sqrt{144} \cdot \sqrt{10}$

Thankfully, $144$ is perfect square, so $\sqrt{144}$ can be reduced to $12$. Since $10$ does not divide evenly into any prefect squares, $\sqrt{10}$ will no simplify.

$12 \sqrt{10}$