Question

Rationalize the denominator!
Question in the picture

Answer 1

A
`(45-5\sqrt7)/(37)`

Explanation:

Easy. First let's multiply numerator and denominator by
`9-\sqrt7` since we will create a difference of squares to get rid of the root, then start doing the calculations

`(10(9-\sqrt7))/((9+sqrt7)(9-\sqrt7))=(10(9-\sqrt7))/(81-7) = (10(9-\sqrt7))/(74) =\\(5(9-\sqrt7))/(37)=(45-5\sqrt7)/(37)`

Answer 2

A

Explanation:

`(10)/(9+√(7) )`

To rationalise the denominator multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 9 +
`√(7)` is 9 -
`√(7)`

=
`(10(9-√(7)) )/((9+√(7))(9-√(7)) )` ← expand denominator using FOIL

=
`(90-10√(7) )/(81-7)`

=
`(90-10√(7) )/(74)` ( divide terms on numerator/ denominator by 2 )

=
`(45-5√(7) )/(37)` → A