HELP!!!! GMAT Question...Show me how to crack it?

Question

Is this difference of two squares...no idea

In this question the there are two quanties to be added, and either quantity is completey under a square root sign so:

what is ( (sqrt of 9 plus the square root of 80 (entire quantity under the square root) plus the sqrt of 9 minus the square root of 80 (entire quantity under the square root) ) squared (in other words after those two are added the answer is squared. I know messy! help!!!

Answer 1

you mean (sqrt(9+sqrt(80)) + sqrt(9-sqrt(80))^2
for simple expression
Let 9+sqrt(80) = x
9-sqrt(80) = y
x+y = 18
xy = 81-80 = 1 (a^2-b^2 formula)
we need(sqrt(x) + sqrt(y)) ^2
= x + y + 2 sqrt(xy)
= 18+ 2 sqrt(1)
= 20

Answer 2

Assuming I interpret your question correctly, Use the binomial expansion and get

(9^1/2 +80^1/2)^1/2^2 +2 (9^1/2+80^1/2)^1/2 * (9^1/2-80^1/2)^1/2 +

(9^1/2 -80^1/2)^1/2^2 which becomes

9^1/2+80^1/2 + 2(9-80)^1/2 + 9^1/2 - 80^1/2 which becomes

3 + 80^1/2 +2(-71)^1/2 +3 - 80^1/2 which becomes
6 + 2(-71)^1/2 You will have an imaginary number
6 + 2i(71)^1/2

Answer 3

Lol... for this I need some more clarification.

Instead of writing out in word form, try giving us the numerical equation, it should make things much clearer.

For the square root you could try putting it in power form, or rather in the form "^(1/2)".

Thanks.

Answer 4

[sqrt{sqrt(9)+sqrt(80)} + sqrt{sqrt(9)-sqrt(80)}]^2
let ur sqrt(9)=x & sqrt(80)=y
we hav now
[sqrt(x+y) + sqrt(x-y)]^2
using(a+b)^2=a^2+b^2+2a*b

(x+y) + (x-y) +2*sqrt[(x+y)*(x-y)]
2x + 2*sqrt(x^2 - y^2)
now putting values of x and y
2*3 + 2*sqrt(9-80)
6+2*sqrt(-71)
6 +2*iota*8.4
6+16.8(iota)

Answer 5

[rt9+rt80]^1/2{rt9-rt80]^1/2
=[(rt9+rt80)rt9-rt80)]^1/2
=[9-80]^1/2
=+/-i rt71

Answer 6

m not getting the question..