LM wrote:

\(\sqrt{3*\sqrt{80}+\frac{3}{9+4*\sqrt{5}}}=?\)

A) \(\sqrt{3*\sqrt{5}}\)

B) 3

C) \(3*\sqrt{3}\)

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

E) \(9+4*\sqrt{5}\)

Though, I am quite comfortable with the method mentioned by Bunuel, I found an alternative way by The

Economist.

\(9 + 4*\sqrt{5}\) will be approx. equal to 9 + 4 x 2 = 17. Hence 3/ 17 will be quite less to contribute towards the value of expression.

\(3\sqrt{80}\) is approx. 3 x 9 = 27. now \(\sqrt{27}\) will be something more than 5.

Now coming to options:

(A)\(\sqrt{3*\sqrt{5}}\) is approx \(\sqrt{6}\) which is quite less than 5. Rejected.

(B) Rejected.

(C) 3 x 1.732 = 5.1 , which is in our desired range.

(D) 3 + 4 =7. Rejected

(E) 9 + 4 x 2 = 17. Rejected.

Hence the correct ans is (C).

If you like this Ballparking method, please press "Kudos".