Nez wrote:

What is \(\frac{\sqrt{1331}}{\sqrt{396} + \sqrt{275}}\) ?

A \(\frac{1}{2}\)

B 1

C \(\sqrt{3}\)

D 2

E \(\frac{2\sqrt3}{2}\)

well I had to look into dictionary to know the meaning of savant.

coming to the problem, almost all options are in simplest form(Integers, Simple fractions of numbers or multiples of root 3).

By these options we can understand that given large numbers in roots will get simplified by cancelling one or the other factor of them.

The smallest term is 275. since this is a multiple of 5 we can divide 275 by 5 to get 55.

Thus we can express 275 as \(5^2*11\)

Thus \(\sqrt{275}=5\sqrt{11}\)

Since there is no option in answer choices which contains \(\sqrt{11}\)

we can guess that this is term which is common among all other terms and is going to get cancelled.

Thus divide 396 by 11 and we get \(36=6^2\) and \(\sqrt{396}=6\sqrt{11}\)

similarly do the same for 1331 and get its square root as \(11\sqrt{11}\)

thus whole fraction becomes

\((11\sqrt{11})\)

-------------------------

\((6\sqrt{11} + 5\sqrt{11})\)

=\(\frac{11}{(6+5)}\) = 1

I hope this helps!

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