How do you rationalize the denominator and simplify 5/(sqrt6+sqrt5)?

1 Answer
George C.
May 10, 2016

5/(sqrt(6)+sqrt(5)) =5sqrt(6)-5sqrt(5)

Explanation:

Use the difference of squares identity:

a^2-b^2=(a-b)(a+b)

with a=sqrt(6) and b=sqrt(5).

Multiply numerator and denominator by sqrt(6)-sqrt(5)

5/(sqrt(6)+sqrt(5))

= (5(sqrt(6)-sqrt(5)))/((sqrt(6)-sqrt(5))(sqrt(6)+sqrt(5)))

=(5(sqrt(6)-sqrt(5)))/(6-5)

=(5(sqrt(6)-sqrt(5)))/1

=5sqrt(6)-5sqrt(5)

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