How do you rationalize the denominator and simplify ( 3sqrt6 + 5sqrt2)/(4sqrt6 - 3sqrt2)?

1 Answer
Mar 23, 2018

(102 + 29sqrt(12))/(78)

Explanation:

color(white)(xx)(3sqrt(6) + 5sqrt(2))/(4sqrt(6) - 3sqrt(2))

= ((3sqrt(6) + 5sqrt(2))(4sqrt(6) + 3sqrt(2)))/((4sqrt(6) - 3sqrt(2))(4sqrt(6) + 3sqrt(2)))

[Multiply Both Numerator and Denominator by (4sqrt(6) + 3sqrt(2))]

=(72 +20sqrt(12) + 9sqrt(12) + 30)/((4sqrt(6))^2 - (3sqrt(2))^2)

= (102 + 29sqrt(12))/(96 - 18)

= (102 + 29sqrt(12))/(78)

Hence explained.