Problem Solving

[sqrt(9+sqrt(80)+sqrt(9-sqrt(80))]^2
A)1
B)9-4sqrt(5)
C)18-4*sqrt(5)
D)18
E)20

I can narrow it down substituting X and Y for each section and using the (X+Y)^2 format but I cant finish it.

Please Help-thank you

Once you cancel the power of 2 and the square root you get
9 + (something)
So you can eliminate A and B.

So the answer has to be C, D or E
Let's write the equation
9 + sqrt(80) + sqrt(9-sqrt(80))

If you want to guess the answer you could say 80 is pretty close to 81 so
sqrt(80) ~= 9
The equation becomes
9 + 9 + sqrt(9-9) = 18 (D)

or if you want to solve the equation more
sqrt(80) = sqrt(16 * 5) = 4 * sqrt(5)
sqrt(5) is approximately 2.2 so the equation becomes
9 + 4 * 2.2 + sqrt(9 - 8.8 )
9 + 8.8 +sqrt(0.2) ~= 18

You can eliminate C which is 18 -2.2 and you can also eliminate E.
So the answer is 18 (choice D)

Thats a good strategy if you are in a hurry towards the end of the test, but the answer is actually 20. I am just trying to make sure I understand the fundamentals in case I run into one of these next week. Thank you for the reply

The actual value is 18.1803399. So, sck159's analysis is correct. The answer should be 18.

https://www.google.com/search?hl=en&q=%2 ... gle+Search

Does that mean the almighty people at GMAC were wrong? or it might mean I copied it down wrong. I took it at the mgmat facility(for real lifelike simulation) so I dont have a log on my computer. But I would still love to see the nitty gritty dirty math involved. Thank you too for replying.

The answer to this one is 20

if you let x = the first segment and y=the second you have a familiar set up (X+Y)^2 which equals x^2+2XY+Y^2 squaring the first and second segments =9+4*sq. rt5 doing the same for Y you get 9-4*sqrt5 the 4*sqrt5 drop out and you are left with 18+2XY so the answer has to be greater than 18 if you continue with the math 2XYyou end up with 2*sqrt1 which is equal to 2 so 18+2=20

drhomler,

Looking at your analysis and the answer of 20 it seems to me that your question has to change a bit.

I think the question should be [sqrt(9 + sqrt(80)) + sqrt(9 - sqrt(80))]^2
Your initial question stem was different.

Please confirm.

yeah you are right-forgot those extra parentheses