Question

rationalize the denominator of:

(4 sqrt3+5sqrt 2)/(sqrt48 +sqrt18)
(5 +sqrt3)/(7-4 sqrt3)

Answer 1

(4 √3+5√2)/(√48 +√18)

= (4 √3+5√2)/(4√3 +3√2) * (4√3 -3√2)(4√3 -3√2)
= (48 - 12√6 + 20√3 - 30)/(48 - 18)
= (18 + 8√6)/30

do the second one in the same way.
multiply top and bottom by 7 + 4√3