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(9*15 + 5*18)^(1/2) =

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broall
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(9*15 + 5*18)^(1/2) = [#permalink] New post   Updated on: 21 Aug 2019, 01:18
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\(\sqrt{9*15 + 5*18} =\)

A. \(3\sqrt{20}\)

B. 15

C. 25

D. \(3\sqrt{20}+3\sqrt{10}\)

E. 34
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B

Originally posted by broall on 22 Apr 2017, 07:12.
Last edited by Bunuel on 21 Aug 2019, 01:18, edited 2 times in total.
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Re: (9*15 + 5*18)^(1/2) = [#permalink] New post   22 Apr 2017, 09:40
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nguyendinhtuong wrote:
\(\sqrt{9\times 15 + 5 \times 18} =\)

A. \(3\sqrt{20}\)
B. \(15\)
C. \(25\)
D. \(3\sqrt{20}+3\sqrt{10}\)
E. 34


Factor everything:

\(\sqrt{3*3*3*5 + 5*2*3*3}\)

Notice you can factor out a 9:

= \(\sqrt{9 * (15 + 10)}\)

= \(\sqrt{(9)(25)}\)

= \(\sqrt{9}\) * \(\sqrt{25}\)

= 3 * 5 = 15. Answer B
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Re: (9*15 + 5*18)^(1/2) = [#permalink] New post   22 Apr 2017, 07:31
sqrt(9*15+5*18)

---> 3 sqrt(15+5*2)
---->3*5
----->15
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Re: (9*15 + 5*18)^(1/2) = [#permalink] New post   22 Apr 2017, 09:49
nguyendinhtuong wrote:
\(\sqrt{9\times 15 + 5 \times 18} =\)

A. \(3\sqrt{20}\)
B. \(15\)
C. \(25\)
D. \(3\sqrt{20}+3\sqrt{10}\)
E. 34



sqrt(9*15+5*18)
= sqrt(135+90)
=sqrt(225)
=15

B) is the answer.
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(9*15 + 5*18)^(1/2) = [#permalink] New post   Updated on: 21 Sep 2021, 17:56
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nguyendinhtuong wrote:
\(\sqrt{9\times 15 + 5 \times 18} =\)

A. \(3\sqrt{20}\)
B. \(15\)
C. \(25\)
D. \(3\sqrt{20}+3\sqrt{10}\)
E. \(34\)



There's a useful rule that says: AB = (2A)(\(\frac{1}{2}\)B) [for more on this, see video below]
So (5)(18) = (10)(9)

We get: √(9 x 15 + 5 x 18) = √(9 x 15 + 10 x 9)
= √[9(15 + 10)]
= √[(9)(25)]
= (√9)(√25)
= (3)(5)
= 15

Answer: B

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 23 Apr 2017, 05:35.
Last edited by BrentGMATPrepNow on 21 Sep 2021, 17:56, edited 1 time in total.
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Re: (9*15 + 5*18)^(1/2) = [#permalink] New post   23 Mar 2018, 00:31
broall wrote:
\(\sqrt{9\times 15 + 5 \times 18} =\)

A. \(3\sqrt{20}\)
B. \(15\)
C. \(25\)
D. \(3\sqrt{20}+3\sqrt{10}\)
E. \(34\)

Source: GMAT Free


\(\sqrt{9\times 15 + 5 \times 18} =\)

Factor out 9,

\(\sqrt{9(15 + 5*2)}\)

\(\sqrt{9 * 25}\)

3 * 5

15 (B)
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Re: (9*15 + 5*18)^(1/2) = [#permalink] New post   26 Mar 2018, 17:43
Expert Reply
broall wrote:
\(\sqrt{9\times 15 + 5 \times 18} =\)

A. \(3\sqrt{20}\)
B. \(15\)
C. \(25\)
D. \(3\sqrt{20}+3\sqrt{10}\)
E. \(34\)


We see that 9 is a common factor of both (9 x 15) and (5 x 18). Simplifying, we have:

√[9 x (15 + 5 x 2)]

√(9 x 25)

√9 x √25

3 x 5

15

Alternate Solution:

√(9 x 15 + 5 x 18)] = √(135 + 90) = √225 = 15

Answer: B
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Re: (9*15 + 5*18)^(1/2) = [#permalink] New post   13 Aug 2019, 03:22
(9*15+5*18)^0.5 = (9*15+10*9)^0.5 = (9(10+15))^0.5 = (9*25)^0.5 = 9^0.5 * 25^0.5 = 3*5 = 15.

The answer is therefore B.

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Re: (9*15 + 5*18)^(1/2) = [#permalink] New post   20 Sep 2019, 02:41
Expert Reply
broall wrote:
\(\sqrt{9*15 + 5*18} =\)

A. \(3\sqrt{20}\)

B. 15

C. 25

D. \(3\sqrt{20}+3\sqrt{10}\)

E. 34


Video Explanation



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Re: (9*15 + 5*18)^(1/2) = [#permalink] New post   11 Oct 2021, 09:18
broall wrote:
\(\sqrt{9*15 + 5*18} =\)

A. \(3\sqrt{20}\)

B. 15

C. 25

D. \(3\sqrt{20}+3\sqrt{10}\)

E. 34

\(\sqrt{9*15 + 5*18}\)

Or, \(\sqrt{3^2*3*5+ 5*3^2*2}\)

Or, \(\sqrt{3^2*5(3 + 2)}\)

Or, \(\sqrt{3^2*5^2}\)

Or, \(3*5 = 15\), Answer must be (B)
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Re: (9*15 + 5*18)^(1/2) = [#permalink]
11 Oct 2021, 09:18
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