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Bunuel
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Bunuel
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Bunuel
\(\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?\)

A. 1.0
B. 1.7
C. 2.0
D. 2.4
E. 3.0

This question can a be a little harder if answers will not be so diverse.
Because now we can calculate roughly
\(\sqrt{48}= 6.9\)

\(\sqrt{7 + 6.9}= 3.8\)

\(3.8-\sqrt{3}=2.1\)

So nearest answer is C.
IMHO if there will be answer with 2.1 and 1.9 than rough calculation will be imposible and task will be more useful.
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\(\sqrt{7 + 6.9}= 3.8\)

I have approximate for root 3 memorized but should I know roughly square root of higher numbers like 14 as well?
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Harley1980
\(\sqrt{7 + 6.9}= 3.8\)

I have approximate for root 3 memorized but should I know roughly square root of higher numbers like 14 as well?

Hi,
No you don't have to, whenever you encounter something of this sort, there would be better ways to do it, as GMAT is not likely to test you \(\sqrt{14}\) etc..

But say you get this kind of problems, you can always approximate..
\(\sqrt{14}=\sqrt{3}*\sqrt{5}\) = 1.7*2.2 = 3.8
so you can work with lower numbers too to get the answer
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For square roots:

1. Find the nearest perfect square

\(\sqrt{14}\) would be \(\sqrt{16}=4\).


2. Divide the original number by the answer

\(14/4=3.5\)


3. Find average of square root of perfect square and your answer in part 2 above

\((3.5+4)/2=3.75\)

This approximation is accurate enough for any GMAT level questions I have come across.

For the example above. Simplify to

\(\sqrt{14} - \sqrt{3} = 3.75-1.7\)

Round down as the original question should have been slightly lower than \(\sqrt{14}\).

Answer = 2.0 (c)
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I think this is a high-quality question and I agree with explanation.
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Great question. Could not figure out that the way Bunuel has solved it.
I guessed the answer in following way though -
48 is close to 49 which is square of 7
Now sqrt of 48 will be around 7
Now it becomes sqrt of (7+7) which srt of 14. It is close to sqrt of 16 which is equal to 4.
Now 4 - sqrt of 3 = 4-1.7 = 2.3

Now answer will be slightly smaller than 2.3 as we considered sqrt of 16 rather than original sqrt of 14.
So answer will be smaller than 2.3 and within given answers, it will be equal to 2.

The way Bunual has solved it is very good. New learning. Thanks.
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I think this is a high-quality question and I agree with explanation. Pretty innovative question, and very close options!
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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I think this is a high-quality question and I agree with explanation.
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I like the solution - it’s helpful.
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I like the solution - it’s helpful.
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