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Which of the following is closest in value to √7.5×32×3125?

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Bunuel
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Which of the following is closest in value to √7.5×32×3125? [#permalink] New post  22 Apr 2018, 22:10
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Which of the following is closest in value to \(\sqrt{7.5*32*3125}\)?

A. 75
B. 85
C. 750
D. 850
E. 7500
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doomedcat
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Re: Which of the following is closest in value to √7.5×32×3125? [#permalink] New post  22 Apr 2018, 23:14
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Bunuel wrote:
Which of the following is closest in value to \(\sqrt{7.5*32*3125}\)?

A. 75
B. 85
C. 750
D. 850
E. 7500


32*7.5 = 240 , factoring 240 = 4^2 * 3 * 5

3125 = 5 * 25* 25

so solving = \(\sqrt{4^2 * 5^2 * 3 * 25^2}\)

= 500 \(\sqrt{3}\)= 860 , so D is closest hence ans
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Re: Which of the following is closest in value to √7.5×32×3125? [#permalink] New post  23 Apr 2018, 18:21
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Bunuel wrote:
Which of the following is closest in value to \(\sqrt{7.5*32*3125}\)?

A. 75
B. 85
C. 750
D. 850
E. 7500


We can approximate

\(\sqrt{7.5*32*32*100}=320\sqrt{7.5}\)

\(\sqrt{7.5}\) approx 2.6

\(32*26=832\)

Answer: D
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Re: Which of the following is closest in value to √7.5×32×3125? [#permalink] New post  08 Sep 2019, 00:59
32: 4*4*2
3125: 25*25*5
4*25 out of the roots and 7.5*2*5 inside the root
= 75
75: 25*3
4*25*5 out and 3 inside
= 500*root of 3 =1.73*500 = 865 = d
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Which of the following is closest in value to √7.5×32×3125? [#permalink] New post  06 Nov 2019, 05:51
Bunuel wrote:
Which of the following is closest in value to \(\sqrt{7.5*32*3125}\)?

A. 75
B. 85
C. 750
D. 850
E. 7500


\(\sqrt{7.5*32*3125}…\sqrt{15/2*32*3125}…\sqrt{15/2*32*3125}…\sqrt{15*16*3125}\)
\(\sqrt{3*4^2*5^2*625}…4*5*25\sqrt{3}…4*5*25*(7/4)…5*25*7\)
\(5*25*7=125*7=700+140+35=875\)

Answer (D)
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Re: Which of the following is closest in value to √7.5×32×3125? [#permalink] New post  21 Nov 2020, 11:15
Bunuel wrote:
Which of the following is closest in value to \(\sqrt{7.5*32*3125}\)?

A. 75
B. 85
C. 750
D. 850
E. 7500


\(\sqrt{7.5*32*3125}\)

= \(\sqrt{7.5*2^5*5^5}\)

= \(100\sqrt{7.5*2*5}\)

= \(100\sqrt{25 * 3}\)

= \(500\sqrt{3}\)

= \(500 * 1.7 = ~850\)

Answer is C.
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Which of the following is closest in value to 7.5×32×3125? [#permalink] New post  17 Feb 2023, 07:43
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Bunuel wrote:
Which of the following is closest in value to \(\sqrt{7.5*32*3125}\)?

A. 75
B. 85
C. 750
D. 850
E. 7500


The idea is NOT to do an exact calculation but try to approximate the value, given that the options are quite far off from one another.

\(\sqrt{7.5*32*3125}\)
= \(\sqrt{8*30*3000}\) approximately
= \(\sqrt{800*30*30}\)
= \(\sqrt{2 * 400*30*30}\)
= 20*30 \(\sqrt{2}\)
= 600 * 1.4 = 840

Hence D

Observe that the square root of 7.5 and that of 8 will be almost the same
The square root of 32 and that of 30 will be almost the same
Also, the square root of 3125 and that of 3000 will be almost the same
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Re: Which of the following is closest in value to 7.5×32×3125? [#permalink] New post  17 Feb 2023, 13:20
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Bunuel wrote:
Which of the following is closest in value to \(\sqrt{7.5*32*3125}\)?

A. 75
B. 85
C. 750
D. 850
E. 7500


The approximate square root of 7.5 is 3 (or a little under)

The approximate square root of 32 is 6 (or a little under)

To determine the approximate square root of 3125, we can break it down to:

√25 x √125 = 5 x √25 x √5 = 5 x 5 x √5 = 25√5, which is around 25 x 2.2 or 55.

Thus, the product of our approximations is 3 x 6 x 55 = 990 (or alittle under), which is closest to answer D.

Also, while 990 may seem high, we must remember that the square root of 7.5 is less than three, and the square root of 32 is less than 6, so it makes sense that the approximate value of the expression comes out to around 850.
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Re: Which of the following is closest in value to 7.5×32×3125? [#permalink] New post  17 Feb 2023, 23:01
3125 x 32 = 100,000

Multiply with 7.5 to get 10,000 x 75

Square rooting tends to halve the number of digits so...

√10,000 x √75 = 100 x 8.5 (approximating as 9^2 = 81)

This results in 850, making D is the correct answer choice
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Re: Which of the following is closest in value to 7.5×32×3125? [#permalink]
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