Question

What is the following quotient 9+sqrt 2/4-sqrt 7

Answer 1

9 + √2 / 4 - √7

Multiply the numerator and denominator by the conjugate.

Exact form:

(36 + 9√ 7 + 4√2 + √14) / 9

or

about 7.69

:)))

Answer 2

`(9+√(2))/(4-√(7))`

multiply by the conjugate of denominator.

`=(9+√(2))/(4-√(7))* (4+√(7))/(4+√(7))`

`=((9+√(2))(4+√(7)))/((4-√(7))(4+√(7)))`

apply formula (a+b)(a-b)=a^2-b^2

`=((9+√(2))(4+√(7)))/((4^2-(√(7))^2))`

`=((9+√(2))(4+√(7)))/(16-7)`

`=((9+√(2))(4+√(7)))/(9)`

`=(36+9 √(7) +4 √(2) + √(14))/(9)`

Hence final answer is
`(36+9 √(7) +4 √(2) + √(14))/(9)`