Question

How do you simplify `sqrt288`?

Answer 1

You can factor the number inside the root:

`sqrt(2*2*2*2*2*3*3)`

However, `2*2*3=12`

Then, you have `sqrt(2*12*12)=sqrt(2*12^2)`.

By definition, when you have a squared number inside the square root, you can take its root out:

final answer: `12sqrt(2)`

Answer 2

In order to simplify `sqrt(288)` factor `288` and look for pairs of factors

`288`
`= 2xx144`
`= 2xxcolor(red)( 12) xx color(red)(12)`
and therefore
`sqrt(288) = sqrt(2xx12^2) = 12sqrt(2)`

If you did not recognize `144` as `12^2` you could have continued the factoring as
`2xx144`
`=2xx2xx72`
`=2xx2xx2xx36`
`=2xx2xx2xx2xx18`
`=2xx2xx2xx2xx2xx9`
`=2xx2xx2xx2xx2xx3xx3`
`=color(red)(2)xxcolor(red)(2)xxcolor(blue)(2)xxcolor(blue)(2)xx2xxcolor(orange)(3)xxcolor(orange)(3)`
So
`sqrt(288) = sqrt(color(red)(2^2)*color(blue)(2^2)*2*color(orange)(3^2))`
`= color(red)(2)*color(blue)(2)*color(orange)(3)sqrt(2)`
`=12sqrt(2)`