How do you rationalize the denominator and simplify 3√5+√6?

1 Answer
Don't Memorise
Jun 12, 2016

=3√6−3√5

Explanation:

3√5+√6

We rationalise the denominator by multiplying the expression by the conjugate of the denominator. √5−√6

3⋅(√5−√6)(√5+√6)⋅(√5−√6)

=3⋅(√5)+3⋅(−√6)(√5+√6)⋅(√5−√6)

=3√5−3√6(√5+√6)⋅(√5−√6)

  • Applying identity
    (a+b)(a−b)=a2−b2 to the denominator.

=3√5−3√6(√5)2−(√6)2

=3√5−3√65−6

=3√5−3√6−1

=−3√5+3√6

=3√6−3√5

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
7437 views around the world
You can reuse this answer
Creative Commons License