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sqrt(9+sqrt(80)) sqrt(9-sqrt(80))=

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sqrt(9+sqrt(80)) sqrt(9-sqrt(80))=

by shaftbond » Sun Aug 07, 2011 3:08 pm
sqrt(9+sqrt(80)) sqrt(9-sqrt(80))=

this was part of a larger problem. i got it down to this and i know what it equals (i looked at the answer) but i don't know how to get there from here. Any help would be appreciated.

The answer is 1
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by beatthegmat.garry » Sun Aug 07, 2011 5:58 pm
We know that sqrt(a)*sqrt(b)=sqrt(ab).

sqrt(9+sqrt(80)) sqrt(9-sqrt(80)=sqrt(9+sqrt(80)*(9-sqrt(80))
=sqrt(9^2-sqrt(80^2)) .................(a+b)(a-b)=a^2-b^2
=sqrt(81-80)
=sqrt(1)
=1

Hope this help :)
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by Anurag@Gurome » Sun Aug 07, 2011 8:28 pm
shaftbond wrote:sqrt(9+sqrt(80)) sqrt(9-sqrt(80))=

this was part of a larger problem. i got it down to this and i know what it equals (i looked at the answer) but i don't know how to get there from here. Any help would be appreciated.

The answer is 1
√(9 + √80)√(9 - √80) = √[(9 + √80)(9 - √80)]
= √[81 - 80) {Apply (a + b)(a - b) = a² - b²}
= √1 = 1
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by shaftbond » Sun Aug 07, 2011 8:28 pm
Yes! That does help. I was forgetting (a+b)(a-b)=a^2-b^2..

Thanks so much!
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