Square roots-help!

Question

How do you solve this?

(\sqrt{9 +\sqrt{80}} * sqrt{9 +\sqrt{80}}) * 2

tl372 · Answer

First, multiply the two square roots together. 

(√ (9+√ 80)*(9-√ 80) ) * 2

Then solve inside the square root:

 = (√ (81 - 80) ) *2
 = (√ 1) *2
 = 2

vibha · Answer

I'm sorry the 2 should be superscripted. The expression is squared.

Professor · Answer

= (√(9 +√80) * √(9 - √80))^2
=1

sm176811 · Answer

The expression boild down to (81-80)*2

Or 1*2 = 2!

sm176811 · Answer

If its superscript then its 1!

Professor · Answer

any explanation??????????????

vibha · Answer

no...it was a gmat prep test question

Yurik79 · Answer

my answer is 2
No way it can be 20))

M8 · Answer

Prof you forgot about 18, the final sum is 2+18, so the answer is  20 .
Here is my detailed solution:

(√(9 +√80) + √(9 - √80))^2 => 
9+√80+9-√80+2*(√(9+√80)*√(9 - √80)) => 
18+2*√(81-9√80+9√80-√6400) =>
18+2*√(81-80) => 18+2*1 => 20.

Hope it's clear.

chiragr · Answer

I guess profs answer is correct

expression is 
(√(9 +√80) * √(9 - √80))^2 

not 

(√(9 +√80) + √(9 - √80))^2

M8 · Answer

Sorry vibha gave us the wrong question.
The correct question is  (√(9 +√80)  +  √ (9 - √80))^2 .

And I solved it again as I solved it in GMATPrep. 
As this question is from GMATPrep. And the OA is 20.
Just use the expression (a+b)^2, for this one. 
Very easy question.

kook44 · Answer

Ah- "+" makes a big difference.

Agree w/ Lenin. 20 it is

Yurik79 · Answer

Ah I see it now))
agree 20 
BTW M8 where are you from?Russia?
Lenin ))

M8 · Answer

Even if I have the Lenin's portrait as avatar it does not mean that I'm from Russia. 
The man on your picture looks like Turk not like Uzbek. :wink:

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