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Re: [square_root]463[/square_root] is between [#permalink]

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12 Aug 2012, 19:27

1

This post was BOOKMARKED

JustinDragna wrote:

The way I solved it was by realizing

20^2= 400

so 21^2 = 20^2 +20 + 1*21 = 441

and

22^2 = 20^2 +20*2 + 2*21 = 440 + 40 + 42 > 500

so \sqrt{463} is >21 but <22

still wasn't that fast, but it made me think there might be some formula or something.

The other way is to find the square root of 463 first and then compare it, but even this method will require atleast 3-4 iterations and is pretty long.

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still wasn't that fast, but it made me think there might be some formula or something.

Your reasoning is perfect. And there is no magic formula to help here.

We can actually avoid the second part. We saw that moving from 20 to 21, the increase was 441-400 = 41. So, moving from 21-22, the increase would definitely be greater than 41. 441+41 > 463. Thus it must lie between 21 and 22.

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(A) 21 and 22 (B) 22 and 23 (C) 23 and 24 (D) 24 and 25 (E) 25 and 26

To determine in which range of numbers the square root of 463 falls, we should start by squaring the smallest number in the answer choices until we find the two perfect squares that 463 falls between:

21^2 = 21 x 21 = 441

22^2 = 22 x 22 = 484

We see that 463 falls between 441 and 484; thus, the square root of 463 must fall between 21 and 22.

Answer: A
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