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It's all in the roots! (Posted on 2004-06-04)

Simplify the following:
√(3 - √5) + √(4 + √7) + √(6 - √35)

No Solution Yet Submitted by Purna

Rating: 3.2857 (7 votes)

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re: answer

| Comment 8 of 9 |

(In reply to answer by K Sengupta)

Let the value of the given expression be n.

Then, we observe that:

n*sqrt(2)
= sqrt(6-2*sqrt(5)) + sqrt(8+2*sqrt(7)) + sqrt(12 - 2*sqrt(35)
= sqrt (sqrt(5) - 1)^2) + sqrt(sqrt(7) + 1)^2) + sqrt(sqrt(7) - sqrt(5))^2)
= sqrt(5) - 1 + sqrt(7) + 1 + sqrt(7) - sqrt(5)
= 2*sqrt 7

Accordingly,
n = sqrt(7)*sqrt(2) = sqrt(14)

Posted by K Sengupta on 2007-04-19 01:34:42

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