# How do you simplify sqrt(1008)?

Apr 3, 2018

$12 \sqrt{7}$

#### Explanation:

The largest perfect root you could pull would be $144$ (${12}^{2}$)

$\frac{1008}{144} = 7$

Apr 3, 2018

The simplified radical is $12 \sqrt{7}$.

#### Explanation:

Simplifying radicals usually uses this rule:

$\textcolor{w h i t e}{=} \sqrt{\textcolor{red}{{a}^{2}} \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{{a}^{2}}} \cdot \sqrt{\textcolor{b l u e}{b}} = \textcolor{red}{a} \sqrt{\textcolor{b l u e}{b}}$

First, write out the factor pairs of $1008$. You can use a calculator or do it by hand, though the latter may take a while. Here they are: Now, look for the biggest square number in the factor pairs.

We can see that the square numbers present are $9$, $16$, $36$, but the biggest one is $144$. Now, split up $1008$ into $144$ and its factor pair, $7$, then use the above rule to simplify the radical:

$\textcolor{w h i t e}{=} \sqrt{1008}$

$= \sqrt{\textcolor{red}{144} \cdot \textcolor{b l u e}{7}}$

$= \sqrt{\textcolor{red}{144}} \cdot \sqrt{\textcolor{b l u e}{7}}$

$= \sqrt{\textcolor{red}{{12}^{2}}} \cdot \sqrt{\textcolor{b l u e}{7}}$

$= \textcolor{red}{12} \cdot \sqrt{\textcolor{b l u e}{7}}$

$= \textcolor{red}{12} \sqrt{\textcolor{b l u e}{7}}$

That's the simplified radical. You can use a calculator to check your work: Hope this helped!