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What is 157609^(1/2)?

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What is 157609^(1/2)?  [#permalink]

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New post Updated on: 20 Jan 2017, 07:50
3
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (00:51) correct 37% (00:38) wrong based on 180 sessions

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What is \(\sqrt{157609}\)?

(A) 323
(B) 378
(C) 392
(D) 397
(E) 403

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Originally posted by hazelnut on 13 Jan 2017, 22:34.
Last edited by hazelnut on 20 Jan 2017, 07:50, edited 2 times in total.
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Re: What is 157609^(1/2)?  [#permalink]

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New post 13 Jan 2017, 23:01
One way to attack this problem is to consider squaring the answer choices. When squared, the right answer will be 157609. We want to minimize calculation, so we want to look for shortcuts.

First, if the square of a number ends in 9 then the number itself will end in 3 or 7. So B and C are gone. We could have also noticed that both B and C are even, so their squares will also be even.

E, 403, is pretty close to a number that's easy to work with, 400, so let's consider E next. 400^2 = 160000, so 403^2 will be bigger still. Our number is smaller, so E is gone.

If we start multiplying A, 323, out the long way we find that the tens digit is 2, not 0. Eliminate.

D is all that's left.
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Re: What is 157609^(1/2)?  [#permalink]

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New post 14 Jan 2017, 00:07
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ziyuenlau wrote:
What is \(\sqrt{157609}\)?

(A) 323
(B) 378
(C) 392
(D) 397
(E) 403


\(300^2 = 9000\)
\(400^2 = 16000\)
\(350^2 = 122500\)

So, The number must be Greater than 350 and the units digit of the number must end in 3 and 7...

Among the given options only (D) fits in perfectly , hence, correct answer must be (D)


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Re: What is 157609^(1/2)?  [#permalink]

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New post 14 Jan 2017, 00:41
157609 is odd so its sq rt cannot be even. Eliminate B,C

Option E is 403, 400 is sq rt of 160000 which is greater than 157609. We are left with 323 and 397. Now 350 square is 122500 so 323 can be eliminated. Hence answer is d 397

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Re: What is 157609^(1/2)?  [#permalink]

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New post 19 Nov 2017, 07:34
Since the units digit has to be 9 so only 323 and 397 will remain, then we can take a square of 320 and determine that 323 will not be our answer coz 320^2= 102400 so therefore D is our answer
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What is 157609^(1/2)?  [#permalink]

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New post 19 Nov 2017, 09:08
hazelnut wrote:
What is \(\sqrt{157609}\)?

(A) 323
(B) 378
(C) 392
(D) 397
(E) 403


\(400^2 = 160000\)
Also, for the last digit 9, the square root could be 3 or 7 because \(\sqrt{49} = 7\) and \(\sqrt{9} = 3\)
Since the number in question is slightly below 160000, the square root cannot be 403.

Therefore, the number must be 397(Option D)

Another method to tests our answer is as follows:
\((397)^2 = (400 - 3)^2 = 160000 + 9 - 2(400)(3) = 160009 - 2400 = 157609\)
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Re: What is 157609^(1/2)?  [#permalink]

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New post 31 May 2018, 01:19
hazelnut wrote:
What is \(\sqrt{157609}\)?

(A) 323
(B) 378
(C) 392
(D) 397
(E) 403


We need a number whose square is 157609.

Answer choice B and C end with even number, therefore these two numbers can't give a number that ends with 9. Eliminate

Choice E is easier. We know 400 * 400 = 160000 (approx), more than our number. Eliminate

A and D, Solve for one on the two numbers and you will get the answer.

(D)
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Re: What is 157609^(1/2)?  [#permalink]

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New post 01 Jun 2018, 11:23
hazelnut wrote:
What is \(\sqrt{157609}\)?

(A) 323
(B) 378
(C) 392
(D) 397
(E) 403


Since we are finding a number that when multiplied by itself will have a units digit of 9, we see that the units digit of that number must either be 3 or 7.

Thus, our only possible answers are A, D, and E.

Since 400 x 400 = 160,000, we see that E is too large..

Since 300 x 300 = 90,000 and 157,609 is much closer to 160,000 than it is to 90,000, we see that its square root should be closer to 400 than to 300, so thus the answer must be 397.

Answer: D
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Re: What is 157609^(1/2)? &nbs [#permalink] 01 Jun 2018, 11:23
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