# is there an easy way to find square root ?

Discussion in 'DAT Discussions' started by joonkimdds, May 28, 2008.

1. ### joonkimdds Senior Member

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if the question says find the square root of 20736, is there an easy way to find the answer?

3. ### doc3232

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So that number is about 20,000 right?
then you can say thats about 200x100 (a little more).
Then a squared number is always bigger than if you added +1 to it and -1 to the other ie:
5x5=25 4x6=24 added +1 to 5 and -1 to the other 5.
So
we know the number is a bit less than (100+200)/2
but we also know that the number is a bit more as we said earlier (we estimated the 20.7k to be 20.0k)
So you just need to use your math skills to estimate a close number.
I estimated 140-145. It is actually 144.
Hope that helps.

4. ### bigstix808 Mac Daddy Member

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to build on the previous post...

&#8730;20763 ~
&#8730;20000 =
&#8730;(2*100*100) =
&#8730;2 * &#8730;100 * &#8730;100 =
&#8730;2 * 10 * 10 =
&#8730;2 * 100 =
1.4 * 100 =
140

i think if you know the approx sqrt of 2 then you could get an answer close to the actual thing

5. ### DRHOYA

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QR is my weakest section by far. When I read the OP's question I was thinking along the same lines as above. I'm sorry Doc, but I lost you when you said (100+200) / 2. I just can't figure out where you are getting that from.

6. ### vvvv

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20736=2x 10^4
sq rt = 1.4 x 10^2

7. ### supraman Boston Celtics

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Just find a number to the near hundreds or thousands place, get that approximate number, then from the answer chooses do the multiplicatation on the same number to see if you get the answer (shouldnt take more than a minute)

8. ### Streetwolf Ultra Senior Member Dentist

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I *highly* doubt you get that, and even if you did, the answers would not be close together.

For a number this size I would look to narrow it down within 100 first. You know 10,000 = 100^2 and 40,000 = 200^2 so it's somewhere in the 100s. I'm just doing this as a check for when I look at my answer.

Come up with some factors. You have 20,736. This divides by 4 into 5,184. This divides by 4 into 1,296. This divides by 4 into 324. This divides by 4 into 81. So you have 4*4*4*4*81 (which happens to be 9^2). So you have 16^2*9^2 and the square root is 16*9 = 144.

I like dividing by 4 because 4 is a square itself and very easy to work with.

Unless you have some ridiculous number you can almost definitely work your way down to a couple perfect squares and a low number square root. Memorize sqrt(2) = 1.41 and sqrt(3) = 1.73.

If you had 20,735 for example you would divide by 5 and get 4,147. I would round to 4,145 and divide by 5 again to get 829. Then I'd round to 830 and divide by 5 to get 166. That's nearly 13^2. So I'd have 5*5*5*13*13 which is 5*13*sqrt(5) which is 65*sqrt(5). You can guess that sqrt(5) is approximately 2.2 and 65*2.2 = 143. That's pretty freakin' close. Again, you might want to try working with the 4s as opposed to what I did up there with the 5s. When I used 5s I had to divide 3 times which left me with a sqrt(5). If I divided by 4 three times, I would still have all perfect squares.

9. ### Optimism Smiles DAT drains my ATP

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Streetwolf you are amazing. Are you sure you don't want to go into teaching?!

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