How do you simplify `sqrt(1008)`?

The largest perfect root you could pull would be `144` (`12^2`)

`1008/144= 7`

Simplifying radicals usually uses this rule:

`color(white)=sqrt(color(red)(a^2)color(blue)b)=sqrtcolor(red)(a^2)*sqrtcolor(blue)b=color(red)asqrtcolor(blue)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:

`color(white)=sqrt(1008)`

`=sqrt(color(red)144*color(blue)7)`

`=sqrtcolor(red)144*sqrtcolor(blue)7`

`=sqrtcolor(red)(12^2)*sqrtcolor(blue)7`

`=color(red)12*sqrtcolor(blue)7`

`=color(red)12sqrtcolor(blue)7`

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

![https://www.desmos.com/calculator]()

Hope this helped!