Check it out:

5 * sqrt(200) = 5 * sqrt(100*2) = 5 * sqrt(100) * sqrt(2) = 5 * 10 * sqrt(2) = 50 * sqrt(2)

Now, since they knew that sqrt(2) is approximately equal to 1.414, they could pop a fairly accurate decimal.  BUT, we're going to just leave it in its pure form since it's more accurate this way!

What we're really doing when we try to rewrite these things is that we are going on a perfect square hunt!

Look at this guy:

sqrt(75)
See any perfect squares hiding in here?

What about 25?

sqrt(75) = sqrt(25*3) = sqrt(25) * sqrt(3) = 5 * sqrt(3)


TRY IT:

Rewrite sqrt(45) so that the smallest number possible is inside the radical.