How do you divide sqrt7/(sqrt34+5)√7√34+5?

1 Answer
Alan P.
Mar 24, 2015

This can be simplified a bit by removing the radical from the denominator.
To do this recall that
(a + b) * (a - b) = (a^2 - b^2)(a+b)⋅(a−b)=(a2−b2)
or, for our particular case
(sqrt(34) + 5) * (sqrt(34) - 5) = 34 -25 = 9(√34+5)⋅(√34−5)=34−25=9

Applying this to the original problem:
sqrt(7)/(sqrt(34)+5)√7√34+5

= sqrt(7)/(sqrt(34)+5) * (sqrt(34)-5)/(sqrt(34)-5)=√7√34+5⋅√34−5√34−5

= ((sqrt(7)) (sqrt(34) - 5))/9=(√7)(√34−5)9

(The numerator could be multiplied but doing so provides not obvious simplification.)

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