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Sub 505 (Easy)|   Arithmetic|   Roots|            
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Bunuel
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
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Bunuel
What is the value of \(\sqrt{17} + \sqrt{47}\), to the nearest whole number?

A. 8
B. 11
C. 12
D. 15
E. 32

\(\sqrt{16} = 4\)
\(\sqrt{25} = 5\)
So, \(\sqrt{17} ≈ 4.1\)

\(\sqrt{36} = 6\)
\(\sqrt{49} = 7\)
So, \(\sqrt{47} ≈ 6.8\)

So, \(\sqrt{17} + \sqrt{47}≈4.1 + 6.8≈10.9\)

Answer: B
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A technique that I adopt when I have to deal with non-perfect square is to think of bigger perfect squares and then introduce decimals.

Now, instead of 17, let’s think of 1700. We know \(40^2\) = 1600 and \(41^2\) = 1681. Therefore, √1700 is just a shade above 41.
It is now easy for you to see that √17 will be a shade above 4.1

Similarly, \(70^2\) = 4900, so √4700 will be very close to 69 (less than 69).
So, √47 will be a shade below 6.9.

Therefore, √17 + √47 ≈ 4.1 + 6.9 = 11.

The correct answer option is B.

Hope that helps!
Aravind B T
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Bunuel
What is the value of \(\sqrt{17} + \sqrt{47}\), to the nearest whole number?

A. 8
B. 11
C. 12
D. 15
E. 32
YO,
So Here Just Check the nearest Roots
\sqrt{16} which is 4 so there is \sqrt{17 } is a bit more than 4 i apporx it as 4.25
\sqrt{49} Which is 7 so here also \sqrt{47} which is <7 may be 6.50 or somthing, where the options are easy so the nearest Number is 11
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