SOLUTION: Please help. Write in simplified radical form by rationalizing the denominator. -2 times the square root of 2+2 / -3 times the square root of 2+5 Thanks.

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Question 190645: Please help.
Write in simplified radical form by rationalizing the denominator.
-2 times the square root of 2+2 / -3 times the square root of 2+5
Thanks.
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
[(-2 sqrt(2) + 2)] / [(-3 sqrt(2) + 5)]
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Multiply numerator and denominator by (-3sqrt(2)-5) to get:
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[(-2 sqrt(2) + 2)(-3sqrt(2)-5)] / [(-3 sqrt(2) + 5)(-3sqrt(2)-5)]
Use FOIL on the numerator and on the denominator to get:
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= [6*2 +(10-6)sqrt(2)] / [9*2-25]
---
= [12 + 4sqrt(2)]/[-7]
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= [-4/7][3+sqrt(2)]
===========================
Cheers,
Stan H.

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