How to Reduce sqrt(264) Mentally – GMAT Quick Math

GMATPill Response

When I see 264 I notice first thing that it’s an even number. If it’s an even number that is divisible by 4, then I can break it up easily since I can do something like sqrt(4) * sqrt(?) = sqrt(264)

The sqrt(4) = 2, that’s easy. So then I would be left with 2*sqrt(?) = sqrt(264)

Well, what’s the question mark?
sqrt(4) * sqrt(?) = sqrt(264)
We need to divide 264 by 4. Take the first two digits 26 and divide it by 4. You can do that 6 times and that would give you 24.

Do your long division. 26-24 = 2
Now add on the 4 digit and you get 24

Divide 24 by 4 and you get 6 agaain.

So the two 6′s give you 66.
So sqrt(4) * sqrt(?) = sqrt(264)
becomes
sqrt(4) * sqrt(66) = sqrt(264)
= 2*sqrt(66)