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# 184,513^(1/2) is between

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Math Expert
Joined: 02 Sep 2009
Posts: 50619
184,513^(1/2) is between  [#permalink]

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31 May 2016, 01:33
00:00

Difficulty:

5% (low)

Question Stats:

82% (00:52) correct 18% (00:52) wrong based on 228 sessions

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$$\sqrt{184,513}$$ is between

(A) 100 and 200
(B) 200 and 300
(C) 300 and 400
(D) 400 and 500
(E) 500 and 600

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Joined: 02 Aug 2009
Posts: 7035
Re: 184,513^(1/2) is between  [#permalink]

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31 May 2016, 02:17
Bunuel wrote:
$$\sqrt{184,513}$$ is between

(A) 100 and 200
(B) 200 and 300
(C) 300 and 400
(D) 400 and 500
(E) 500 and 600

Hi
to find the square, put the digits in pair ...
18,45,13...
so we are looking at $$\sqrt{18}$$ as the first digit = between $$4^2$$ and $$5^2$$..
there are two pairs of number which can be taken as two digits after 4,..
so our answer has to be between 400 and 500..
D
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Re: 184,513^(1/2) is between  [#permalink]

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31 May 2016, 22:43
1
1
Bunuel wrote:
$$\sqrt{184,513}$$ is between

(A) 100 and 200
(B) 200 and 300
(C) 300 and 400
(D) 400 and 500
(E) 500 and 600

Another method is to start with the options.

Look at (A). 200^2 = 40,000 which is much lower than 184,513
Going down the options, you will see that 500^2 = 250,000 which is the first one greater than 184,513.
Hence, answer will be between 400 and 500. Answer (D)
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184,513^(1/2) is between  [#permalink]

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01 Jun 2016, 11:38
1
Bunuel wrote:
$$\sqrt{184,513}$$ is between

(A) 100 and 200
(B) 200 and 300
(C) 300 and 400
(D) 400 and 500
(E) 500 and 600

Clear (D) , check using the options -

(A) 100 and 200

200^2 = 40000 < 184513

(B) 200 and 300

300^2 = 90000 < 184513

(C) 300 and 400

400^2 = 160000 < 184513

(D) 400 and 500

500^2 = 250000 > 184513

400^2 = 160000 < 184513

(E) 500 and 600

600^2 = 360000 > 184513

500^2 = 250000 > 184513

Hence among the given options only (D) is correct...

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Re: 184,513^(1/2) is between  [#permalink]

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01 Jun 2016, 13:27
Such questions are better solved by trying options and when it is not clear which option to try first then better start with option C. I straightaway tried option D as square of 400 is 16000 which is less than 184513 and square of 500 is 25000 is greater than 184513.
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Re: 184,513^(1/2) is between  [#permalink]

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11 Oct 2017, 12:14
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Re: 184,513^(1/2) is between &nbs [#permalink] 11 Oct 2017, 12:14
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# 184,513^(1/2) is between

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