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# QOTD#17 Which of the following is closest to

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QOTD#17 Which of the following is closest to [#permalink]  12 Sep 2016, 11:58
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Question Stats:

50% (01:33) correct 50% (00:51) wrong based on 16 sessions
Which of the following is closest to $$\sqrt{(2.3)(10^9)}$$?

A. 50,000
B. 150,000
C. 500,000
D. 1,500,000
E. 5,000,000

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[Reveal] Spoiler: OA

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1654 [2] , given: 396

Re: QOTD#17 Which of the following is closest to [#permalink]  12 Sep 2016, 12:04
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Expert's post
Explanation

The expression $$\sqrt{2.3 * 10^9}$$ can be simplified as follows.

$$\sqrt{2.3 * 10^9}$$ =$$\sqrt{2.3 * 10* 10^8}$$

=$$\sqrt{23 * 10^8}$$=$$10^4*\sqrt{23}$$.

Since $$\sqrt{23}$$is between 4 and 5, it follows that $$10^4*\sqrt{23}$$ is between 40,000 and 50,000.

Therefore, of the five answer choices listed, 50,000 is closest to $$\sqrt{2.3 * 10^9}$$. The correct answer
is Choice A.
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Re: QOTD#17 Which of the following is closest to [#permalink]  19 Sep 2016, 17:11
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sandy wrote:
Which of the following is closest to $$\sqrt{2.3 * 10^9}$$?

A. 50,000
B. 150,000
C. 500,000
D. 1,500,000
E. 5,000,000

Always scan the answer choices BEFORE performing any calculations.
Since the answer choice are very spread apart, we can be very aggressive with our estimation.

We're going to use a nice rule that says √(ab) = (√a)(√b)

We have √(2.3 x 10⁹)
Since 2.3 isn't an easy number to find the square root of, the above rule doesn't help us much.
However, what if we do the following:
√(2.3 x 10⁹) = √(2.3 x 10¹ x 10⁸)
= √(23 x 10⁸)

How does this help?
Well, 23 is pretty close to 25 and we know that √25 = 5.
Can we do this? You bet. Remember that since the answer choice are very spread apart, we can be very aggressive with our estimation

We get:
√(23 x 10⁸) = (√23)(√10⁸)
≈ 5(10⁴)
≈ 5(10,000)
≈ 50,000

Cheers,
Brent
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Re: QOTD#17 Which of the following is closest to [#permalink]  11 Aug 2017, 10:38
well i did it differently,
i checked the answers and i squared the first and divided it by 2.3 and fount out that it's the closest to 10^9, all the other are just way off
though i guess it may not work as well
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Re: QOTD#17 Which of the following is closest to [#permalink]  21 Aug 2017, 09:29
If we have a problem 10^4, is not the solution 100,000? Since the decimal point is in the end of 10. so we carry the point 4 step right.
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Re: QOTD#17 Which of the following is closest to   [#permalink] 21 Aug 2017, 09:29
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