Question

Show that
`(5+2root3)/(2+root3)` can be written as 4-root3

Answer 1

see explanation

Explanation:

`(5+2√(3) )/(2+√(3) )`

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

the conjugate of 2 +
`√(3)` is 2 -
`√(3)` , then

=
`((5+2√(3))(2-√(3)) )/((2+√(3))(2-√(3)) )` ← expand numerator/ denominator using FOIL

=
`(10-5√(3)+4√(3)-6 )/(4-2√(3)+2√(3)-3 )`

=
`(4-√(3) )/(1)`

= 4 -
`√(3)`