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Which of the following is greatest?

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Which of the following is greatest? [#permalink]

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Which of the following is greatest?

A. \(10\sqrt{3}\)

B. \(9\sqrt{4}\)

C. \(8\sqrt{5}\)

D. \(7\sqrt{6}\)

E. \(6\sqrt{7}\)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Jun 2017, 12:47, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Which of the following is greatest? [#permalink]

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New post 17 Jun 2017, 09:52
A.
Other option have a simultaneous increase in denominator and decrease in denominator.

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AbdurRakib wrote:
Which of the following is greatest?

A. \(10\sqrt{3}\)

B. \(9\sqrt{4}\)

C. \(8\sqrt{5}\)

D. \(7\sqrt{6}\)

E. \(6\sqrt{7}\)


We can use a nice rule that says (√x)(√y) =√(xy)
Also, we'll rewrite each integer as a root.
For example 10 = √100

So, we get...
A) 10√3 = (√100)(√3) = √300
B) 9√4 = (√81)(√4) = √324
C) 8√5 = (√64)(√5) = √320
D) 7√6 = (√49)(√6) = √294
E) 6√7 = (√36)(√7) = √252

√324 is the greatest

Answer:
[Reveal] Spoiler:
B


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Re: Which of the following is greatest? [#permalink]

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New post 28 Jun 2017, 08:19
AbdurRakib wrote:
Which of the following is greatest?

A. \(10\sqrt{3}\)

B. \(9\sqrt{4}\)

C. \(8\sqrt{5}\)

D. \(7\sqrt{6}\)

E. \(6\sqrt{7}\)


A. 10*1.732 = 17.32
B. 9*2 = 18
C. 8*2.XX = 16.XX
D. 7*2.XX = 14.XX
E. 6*2.XX = 12.XX

Hence, correct answer will be (B)
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Re: Which of the following is greatest? [#permalink]

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New post 28 Jul 2017, 03:51
BeingHan wrote:
A.
Other option have a simultaneous increase in denominator and decrease in denominator.

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i think you misunderstood the ques.
it is not division., it is square root.
integer* sq.root of an integer
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Re: Which of the following is greatest? [#permalink]

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New post 24 Sep 2017, 02:17
B. is the answer

A.) square it = 300
B.) square it = 324
C.) square it = 320
D.) square it = 294
E.) square it = 252

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Re: Which of the following is greatest? [#permalink]

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AbdurRakib wrote:
Which of the following is greatest?

A. \(10\sqrt{3}\)

B. \(9\sqrt{4}\)

C. \(8\sqrt{5}\)

D. \(7\sqrt{6}\)

E. \(6\sqrt{7}\)


Let’s estimate √3, √5, √6, and √7.

√3 ≈ 1.7

√5 ≈ 2.2

√6 ≈ 2.4

√7 ≈ 2.7

Thus:

A) 10 x 1.7 = 17

B) 9 x 2 = 18

C) 8 x 2.2 = 17.6

D) 7 x 2.4 = 16.8

E) 6 x 2.7 = 16.2

Alternate Solution:

Another way to get rid of the roots to compare each answer is to square each answer choice:

A) (10√3)^2 = 100 x 3 = 300

B) (9√4)^2 = 81 x 4 = 324

C) (8√5)^2 = 64 x 5 = 320

D) (7√6)^2 = 49 x 6 = 294

E) (6√7)^2 = 36 x 7 = 252

Answer: B
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Re: Which of the following is greatest?   [#permalink] 15 Nov 2017, 16:58
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