Question

Simplify by rationalize the denominator 4 root 3 + 5 root 2 / root 48 + root 18

Answer 1

Please see the attachment

Answer 2

AHOY!!

given :- (4√3 + 5√2)/(√48 + √18)

√48 can be written as = 4√3 and √18 can be written as = 3√2

=> (4√3 + 5√2)/(4√3 + 3√2)

=> (4√3 + 5√2)/(4√3 + 3√2) × (4√3 -3√2)/(4√3 - 3√2)

=> (4√3 + 5√2)(4√3 - 3√2)/(4√3 + 3√2)(4√3 -3√2)

=> [4√3(4√3 - 3√2) + 5√2(4√3 - 3√2)]/[(4√3)² - (3√2)²]

=> (48 - 12√6 + 20√6 - 30)/(48 - 18)

=> (18 + 8√6)/30

=> (9 + 4√6)/15

HOPE THIS HELPS!!