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

Question

Which of the following is closest in value to  \sqrt{7.5*32*3125} ?

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

doomedcat · Accepted Answer

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

aserghe1 · Answer

We can approximate

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

\sqrt{7.5}  approx 2.6

32*26=832

Answer: D

LATIFA221B · Answer

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

exc4libur · Answer

\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)

Basshead · Answer

\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.

sujoykrdatta · Answer

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

ScottTargetTestPrep · Answer

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.

achloes · Answer

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

bumpbot · Answer

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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