SOLUTION: How do I rationalise denominators?? :( I mean things like (√2 + 2√5)/(√5 - √2) Thanks!

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Question 556263: How do I rationalise denominators?? :(
I mean things like (√2 + 2√5)/(√5 - √2)
Thanks!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
in general, you multiply the numerator and denominator by the radical from the denominator
___ this "deradicalizes" (is that a word?) the denominator and maintains the value of the fraction

in the example you give, multiplying by the conjugate is the best technique

multiplying by (√5 + √2)/(√5 + √2) ___ [(√2 + 2√5) (√5 + √2)] / [(√5 - √2) (√5 + √2)]

FOILing ___ (√10 + 2 + 10 + 2√10) / (5 + √10 - √10 - 2) ___ (12 + 3√10) / 3 ___ 4 + √10