Here's a trickier one:

sqrt(588)

There are two perfect squares hiding in here...

We'll need to completely factor this thing to find them.

sqrt(588) = sqrt(4*49*3) = sqrt(4) * sqrt(49) * sqrt(3) = 2 * 7 * sqrt(3) = 14 * sqrt(3)


*You can check to see if this is right by
popping sqrt(588) and 14 * sqrt(3) into your calculator... 
You should get the same thing.


TRY IT:

Rewrite sqrt(1575) so that the smallest number possible is inside the radical.


You can do this with other kinds of roots too -- like cube roots.

Check it out:

We'll be on a perfect cube hunt this time!

( cube root of 56 ) = ( cube root of (8*7) ) = ( cube root of 8 )( cube root of 7 ) = 2 * ( cube root of 7 )
 


TRY IT:

Rewrite  cube root of 54 so that the smallest number possible is inside the radical.