Evaluating radical expressions - Please Help ASAP

[postroske]

I am taking the GMAT tomorrow and felt prepared until I saw this question on the GMAT's software practice test. I can not figure out how to properly evaluate this expression.

(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2

the ^2 indicates that the entire expression is to the second power or squared. I can not figure it out and would like to know before i go in tomorrow. If you can, please explain method.

Thanks!

[karthikgmat]

9 can be written as sqrt(5)^2+sqrt(4)^2 and sqrt(80) can be written as sqrt( 4*4*5)
it is square of (a+b)

so the first term is sqrt(5)+2
second term is sqrt(5) -2
adding two we get 2 sqrt(5)

finally squaring that 4*5 =20

..is it ok?

[nikilnikil]

this expression is of the form

(a+b)^2 = a^2+b^2+2*a*b

sqrt(9+sqrt(80)) ^2 + sqrt(9-sqrt(80))^2 + 2* sqrt((9+sqrt(80))*(9-sqrt(80))

= 9+sqrt(80) + 9 - sqrt(80) + 2 * (81-80) [because (a+b)(a-b) = a^2 -b^2]
=9+9+2 = 20

~Nik

[postroske]

thank you both. great explanation!!