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Square root mania

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Master | Next Rank: 500 Posts
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by LSB » Tue Aug 19, 2008 1:03 pm
Hi folks - I'm wondering if anybody can put some sense into this. With a calculator this is no problem. Just wondering whether anybody can point to a fast way.

((9+80^0.5)^0.5+(9-80^0.5)^0.5)^2

a 1
b 9 - 4 * (5) ^ .5
c 18 - 4 * (5) ^ .5
d 18
e 20

OA E
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by pepeprepa » Tue Aug 19, 2008 1:21 pm
Hope you know: a^0.5=sqrt(a)

X=((9+80^0.5)^0.5+(9-80^0.5)^0.5)²
Use this: (a+b)²=a² + 2ab + b²
X= 9 + sqrt(80) + 2*sqrt((9+80^0.5)(9-80^0.5)) + 9 - sqrt(80)
Use this: (a+b)(a-b)=a² - b²
X=18 + 2*sqrt(9²-80)
X=18 + 2*sqrt(1)
You know sqrt(1)=1
X=20
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by LSB » Tue Aug 19, 2008 2:03 pm
Thanks ... I saw the first one. But wasn't able to see this step

Use this: (a+b)(a-b)=a² - b²
X=18 + 2*sqrt(9²-80)

Now I get it. Thanks again.
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very nice!!

by redpen » Sat Sep 06, 2008 2:19 pm
I had to stare at this for like 10 minutes but it is so clear now. Quite simple when you see it!!
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OA E

by karthikgmat » Sun Sep 07, 2008 1:30 am
20 is ans

its very
sqrt(9+sqrt(80)) = sqrt(5)+2
simliarlry sqrt(9-sqrt(80))= sqrt(5)-2
adding those two we get 2sqrt(5)
its square is 20..
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