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December 22, 2014

December 22, 2014

Posted by **lovemath** on Sunday, June 5, 2011 at 9:39pm.

sqrt((2-sqrt3))/sqrt((2+sqrt3))

the answer is 2-sqrt3

but I don't know how they arrive at it.

- trig -
**MathMate**, Sunday, June 5, 2011 at 10:14pmMultiply both the numerator and denominator by the conjugate, sqrt((2-sqrt3))

Then

sqrt(2-sqrt3)/sqrt(2+sqrt3)

=sqrt(2-sqrt3)sqrt(2-sqrt3)/(sqrt(2+sqrt3)sqrt(2-sqrt3))

=sqrt((2-sqrt3)²)/sqrt(2²-3)

=(2-sqrt(3))/sqrt(4-1)

=(2-sqrt(3))/sqrt(1)

=2-sqrt(3)

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