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# 463^(1/2) is between

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Intern
Joined: 10 Aug 2012
Posts: 5

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12 Aug 2012, 08:31
2
4
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:30) correct 11% (00:39) wrong based on 396 sessions

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$$\sqrt{463}$$ is between

(A) 21 and 22
(B) 22 and 23
(C) 23 and 24
(D) 24 and 25
(E) 25 and 26
Intern
Joined: 10 Aug 2012
Posts: 5

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12 Aug 2012, 08:35
1
2
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.
Director
Joined: 22 Mar 2011
Posts: 601
WE: Science (Education)

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12 Aug 2012, 08:58
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.

Your reasoning is perfect. And there is no magic formula to help here.
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Manager
Joined: 05 Jul 2012
Posts: 69
Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)

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12 Aug 2012, 18:27
1
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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Location: India
Concentration: General Management, Technology
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08 Sep 2014, 22:52
2
$$21^2 = 441$$

$$22^2 = 484$$

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Manager
Joined: 11 Oct 2013
Posts: 106
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31

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09 Dec 2015, 05:49
1
EvaJager wrote:
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.

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.

+Kudos, if this helped!
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06 Jan 2017, 09:58
JustinDragna wrote:
$$\sqrt{463}$$ is between

(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.

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Director
Joined: 02 Sep 2016
Posts: 688

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22 Jun 2017, 05:58
The best way is to find the squares and select the correct option.
21^2=441
22^2=484

(A) 21 and 22
(B) 22 and 23
(C) 23 and 24
(D) 24 and 25
(E) 25 and 26
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Help me make my explanation better by providing a logical feedback.

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Manager
Joined: 05 Nov 2014
Posts: 107
Location: India
Concentration: Strategy, Operations
GMAT 1: 580 Q49 V21
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22 Jun 2017, 09:51
21^2=441.
22^2=484.

Therefore OA=A
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Schools: ISB '19, IIMA , IIMB, XLRI
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22 Jun 2017, 21:56
2
JustinDragna wrote:
$$\sqrt{463}$$ is between

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

What is the fastest way to solve this problem?

Square of $$20 = 400$$

Adding $$(21 + 20)$$ to $$400$$ will give us the next square.

$$400 + 20 + 21 = 441 ----$$ (Square of $$21$$)

Adding $$(21 + 22)$$ to $$441$$ will give us the next square.

$$441 + 21 + 22 = 484 ------$$ (Square of $$22$$)

$$\sqrt{463}$$ should be between $$21$$ and $$22$$. Answer (A) ...

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15 Jul 2017, 05:54
Choice:A
I guess these rarely appear on GMAT and it appears if you are scoring something below Q30 for this I suggest
Memorize
Squares till 30 and Cubes till 15 it will make life much easy and also help in related other questions
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Joined: 04 Jan 2015
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28 Oct 2018, 12:46

Solution

Given:
• √463

To find:
• The value of √463 is between which two number.

Approach and Working

• In all the option, the possible value of √463 can only be a non-integer.
o So, we can not find the square root of 463 by prime factorization.
• Let us apply another method.

The perfect square just less than 463 is 441.
• $$21^2$$= 441
The perfect square just greater than 463 is 484.
• $$22^2$$= 484.

Thus, the value of √463 is between 21 and 22.

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Re: 463^(1/2) is between &nbs [#permalink] 28 Oct 2018, 12:46
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