How do you rationalize the denominator and simplify 3/(sqrt[6] – sqrt[3])?

1 Answer

sqrt(6)+sqrt(3)

Explanation:

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

Using this principle:

Multiply by 1 but in the form of 1=(sqrt(6)+sqrt(3))/(sqrt(6)+sqrt(3))

(3(sqrt(6)+sqrt(3)))/((sqrt(6)-sqrt(3))times(sqrt(6)+sqrt(3))

=(3sqrt(6)+3sqrt(3))/((sqrt(6))^2-(sqrt(3))^2)

=(cancel(3)sqrt(6)+cancel(3)sqrt(3))/cancel(3)

=sqrt(6)+sqrt(3)