Rationalise the denominator \frac{1}{4-\sqrt-{11} }

Question

Rationalise the denominator
`\frac{1}{4-\sqrt-{11} }`

Answer 1

`(4+√(11) )/(5)`

Explanation:

to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 4 -
`√(11)` is 4 +
`√(11)` , then

`(1(4+√(11)) )/((4-√(11))(4+√(11)) )` ← expand denominator using FOIL

=
`(4+√(11) )/(16-11)`

=
`(4+√(11) )/(5)`