another gmat prep prob....

[willbeatthegmat]

{√(9+√80) + √(9-√80)}^2 = ?

a) 1
b) 9-4√5
c)18-4√5
d)18
e)20

OA: e

[parallel_chase]

[√(9+√80) + √(9-√80)]^2

expand (a+b)^2 = a^2 + b^2 + 2ab

here is link which explains this process

https://www.beatthegmat.com/please-help-t9145.html

[tritrantran]

{√(9+√80) + √(9-√80)}^2 = ?

a) 1
b) 9-4√5
c)18-4√5
d)18
e)20

OA: e

First we can look at the answer choices and eliminate A and B by estimating the answer. That leaves C, D, and E.

{√(9+√80) + √(9-√80)}^2

sqrt(80) = sqrt (16*5) = 4sqrt(5)

(sqrt[9+4sqrt(5)] + sqrt[9-4sqrt(5)])^2

let x = sqrt[9+4sqrt(5)]

y = sqrt[9-4sqrt(5)]

(x+y)^2 = x^2 + 2xy + y^2

= 9+4sqrt(5) + 2xy + 9-4sqrt(5)
= 18 + a little more

E