How do you divide #sqrt7/(sqrt34+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)#
or, for our particular case
#(sqrt(34) + 5) * (sqrt(34) - 5) = 34 -25 = 9#

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

#= sqrt(7)/(sqrt(34)+5) * (sqrt(34)-5)/(sqrt(34)-5)#

#= ((sqrt(7)) (sqrt(34) - 5))/9#

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

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1618 views around the world
You can reuse this answer
Creative Commons License