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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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Updated on: 17 Jun 2017, 12:47
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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. $$6\sqrt{7}$$

Originally posted by AbdurRakib on 17 Jun 2017, 09:49.
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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17 Jun 2017, 12:52
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Which of the following is greatest?

A. $$10\sqrt{3}=\sqrt{100*3}=\sqrt{300}$$

B. $$9\sqrt{4}=\sqrt{81*4}=\sqrt{324}$$

C. $$8\sqrt{5}=\sqrt{64*5}=\sqrt{320}$$

D. $$7\sqrt{6}=\sqrt{49*6}=\sqrt{294}$$

E. $$6\sqrt{7}=\sqrt{36*7}=\sqrt{252}$$

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

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

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

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28 Jun 2017, 07:26
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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

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

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28 Jun 2017, 08:19
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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. $$6\sqrt{7}$$

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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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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24 Sep 2017, 02:17

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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15 Nov 2017, 16:58
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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

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

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17 Nov 2018, 00:15
Bunuel wrote:
Which of the following is greatest?

A. $$10\sqrt{3}=\sqrt{100*3}=\sqrt{300}$$

B. $$9\sqrt{4}=\sqrt{81*4}=\sqrt{324}$$

C. $$8\sqrt{5}=\sqrt{64*5}=\sqrt{320}$$

D. $$7\sqrt{6}=\sqrt{49*6}=\sqrt{294}$$

E. $$6\sqrt{7}=\sqrt{36*7}=\sqrt{252}$$

HI Bunuel,

I squared all the answer choices and then reached my result. Is that method correct?
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Re: Which of the following is greatest?  [#permalink]

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17 Nov 2018, 00:24
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Yes, it is correct. Since all the numbers are greater than 1, the square of a greater number will be greater.

Best,

rever08 wrote:

HI Bunuel,

I squared all the answer choices and then reached my result. Is that method correct?

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

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17 Nov 2018, 02:32
Abhishek009 wrote:
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)

There is a bit of a problem with this method.

8 * 2.XX needn't necessarily be 16.YY

In fact, 8*2.3 = 18.4
8*2.6 = 20.8
8*2.9 = 23.2
and so on...

So check the method used by Bunuel above.
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Re: Which of the following is greatest?  [#permalink]

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17 Nov 2018, 02:51
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. $$6\sqrt{7}$$

B is correct answer as 9*4^1/2=9*2=18

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

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02 Dec 2019, 08:40
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Re: Which of the following is greatest?   [#permalink] 02 Dec 2019, 08:40
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