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Difficulty:
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Question Stats:
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If \(\sqrt{12}+\sqrt{108}=\sqrt{N}\), then N =
(A) 96
(B) 120
(C) 144
(D) 192
(E) 288
Kudos for a correct solution.
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(A) 96
(B) 120
(C) 144
(D) 192
(E) 288
Kudos for a correct solution.
_________________
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Bunuel
\(\sqrt{12}+\sqrt{108}=\sqrt{N}\)
\(\sqrt{12}+\sqrt{12*3*3}=\sqrt{N}\)
\(\sqrt{12}+3 \sqrt{12}=\sqrt{N}\)
\(4\sqrt{12}=\sqrt{N}\)
N=192
ANSWER D
General Discussion
\((\sqrt{12}+\sqrt{108}) (12[/square_root]+\sqrt{108})=N\)
120 + 2×3×3×4 = N
N=192
Answer: D
120 + 2×3×3×4 = N
N=192
Answer: D
Bunuel
there are two ways ,
1) \(\sqrt{12}+\sqrt{108}=\sqrt{N}\)....
N=12+108+2\(\sqrt{12}*\sqrt{108}\)=120+2*12*3=192..
2)\(\sqrt{12}\)=nearly 3.5(between 9 &16)..
\(\sqrt{108}\) =nearly 10.4(between 100&121)..
so 3.5+10.4=13.9..
ans should be between 13^2 and 14^2.. only D is possible
ans D
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Schools: Cambridge'16
Posts: 405
12=2*2*3
108=2*2*3*3*3
we have
2*sqrt3+6*sqrt3=8*sqrt3
8*sqrt3=8^2*3=192
D
108=2*2*3*3*3
we have
2*sqrt3+6*sqrt3=8*sqrt3
8*sqrt3=8^2*3=192
D
EMPOWERgmatRichC
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Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,775
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GMAT 1: 800 Q51 V49
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Expert reply
Hi All,
The answer choices to this question are sufficiently 'spread out' that we can avoid most of the 'technical math' and use estimation to get to the correct answer.
Root(12) is between 3 and 4
Root(108) is between 10 and 11
The correct answer has to be BETWEEN 10+3=13 and 4+11=15
13^2 = 169
15^2 = 225
So we're looking for an answer between 169 and 225....There's only one that fits....
Final Answer:
GMAT assassins aren't born, they're made,
Rich
The answer choices to this question are sufficiently 'spread out' that we can avoid most of the 'technical math' and use estimation to get to the correct answer.
Root(12) is between 3 and 4
Root(108) is between 10 and 11
The correct answer has to be BETWEEN 10+3=13 and 4+11=15
13^2 = 169
15^2 = 225
So we're looking for an answer between 169 and 225....There's only one that fits....
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Bunuel
+1 for D.
2 Root 3+6Root 3=8 Root 3= Root N
Square Both sides,
64*3=N=192
Bunuel
MAGOOSH OFFICIAL SOLUTION:
First of all, the mistake: we CANNOT add through
Attachment:
cgpwe_img20.png [ 1.32 KiB | Viewed 7431 times ]
That incorrect thinking would lead to the trap answer of (B). Instead, we have to simplify each square root on the left.
Attachment:
cgpwe_img21.png [ 5.29 KiB | Viewed 7454 times ]
Answer = (D).
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Joined: 27 Dec 2012
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\(\sqrt{12}+\sqrt{108}=\sqrt{N}\)
Squaring both sides
\(n = 12 + 108 + 2\sqrt{12*108} = 120 + 72 = 192\)
Answer = D
Squaring both sides
\(n = 12 + 108 + 2\sqrt{12*108} = 120 + 72 = 192\)
Answer = D
Really like lucky's and bunuels approach ...way to go!!!
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GMAT loosers are born not made !!!
Bunuel
\(\sqrt{12}+\sqrt{108}=\sqrt{N}\)
\(\sqrt{12}\) is approx 3.5
\(\sqrt{108}\)=\(\sqrt{N}\) is approx 10.5
Adding both we get, 3.5 + 10.5 = 14
Therefore 14 =\(\sqrt{N}\)
\(N = (14)^2\)
\(N = 196\)
(D) is the nearest
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GMAT 1: 760 Q51 V42
Posts: 10,057
Sqrt of 12 is 3.x and sqrt of 108 is 10.x
Adding both will lead us to a sqrt of close to 14. Therefore, N should be 192.
Answer D
Adding both will lead us to a sqrt of close to 14. Therefore, N should be 192.
Answer D
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