Square root of larger numbers

[Guest]

Hi - I'm pretty good with roots, exponents, factoring but just got an answer wrong because I bogged down on extracting the square root of a large number - it was a perfect square but I just did not see it.

Eg; square root of 576 = 24 but I never saw it. Can someone breakdown the mechanics when face with large numbers that are perfect squares & large numbers that aren't perfect squares.

Thanks!

[StaceyKoprince]

First, you should have all of your squares memorized to 20, and you should also memorize 25 and 30. You should also have your cubes memorized to 5.

Second: break the number down into its prime factors. Start by dividing by the smallest working prime (in this case, 2) and keep going until the number gets small enough that you can break it down more quickly.

576/2 = (500+76)/2 = 250+38 = 288
288/2 = 144
144/2 = 72
72/2 = 36
36 here I might notice that I can chop this down more quickly: 6*6 = 2*3*2*3

So now I've got: 2, 2, 2, 2, 2, 3, 2, 3
For every matching pair, cross off one. Leaves me with:
2,2,2,3
Multiply to get 24.

But if you memorize the squares and cubes I mentioned above, there's a pretty good chance you won't need to use the above process on the test. Also, go back and check that problem - was there something within the problem or the answer choices that could've clued you in to what was going on? Answer choices often contain a LOT of useful directional info if you think about them!

[Guest]

Thanks - appreciate it! Good advice on the memorization.

[rfernandez]

We're glad it helped!