Question

simplify by rationalizing the denominator 4√3+5√2 /√48+√18

Answer 1

√48+√18=4√3+3√2
now
4√3+5√2 /√48+√18
=4√3+3√2 +2√2/4√3+3√2
=1+(2√2/4√3+3√2)
=1+(2√2(4√3-3√2)/30))
=15+4√6-3/15
=12+4√6/15
=(4/15)(3+√6)

Answer 2

4√3+5√2/√48+√18
= 4√3+5√2/4√3+3√2
= (4√3+5√2)(4√3-3√2)/(4√3)^2-(3√2)^2
= 48-12√6+20√6-30/48-18
= 18+8√6/30
= 2(9+4√6)/30
= 9+4√6/15.