SOLUTION: [SQRT (8) + SQRT (16)] / [SQRT (8) + SQRT (81)]

Question 307168: [SQRT (8) + SQRT (16)] / [SQRT (8) + SQRT (81)]
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
[SQRT (8) + SQRT (16)] / [SQRT (8) + SQRT (81)] =
(sqrt(4*2) + 4)/(sqrt(4*2) + 9) =
2*sqrt(2) + 4 / 2*sqrt(2) + 9
Multiply numerator and denominator by 2*sqrt(2) - 9:
(2*sqrt(2) + 4)*(2*sqrt(2) - 9)/ (2*sqrt(2) + 9)*(2*sqrt(2) - 9)) =
(4*sqrt(2)^2 - 18*sqrt(2) + 8*sqrt(2) - 36)/(4*sqrt(2)^2 - 81) =
(4*2 - 10*sqrt(2) - 36)/(4*2 - 81) =
(8 - 10sqrt(2) - 36)/ (8 - 81)
(-10*sqrt(2) - 28)/-73 =
(28 + 10 sqrt(2))/73

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