Question

The simplest form of the expression sqr3-sqr6/sqr3+sqr6?

Answer 1

1 -
`(2√(2) )/(3)`

Explanation:

`(√(3)-√(6) )/(√(3)+√(6) )`

rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

the conjugate of
`√(3)` +
`√(6)` is
`√(3)` -
`√(6)`

=
`((√(3)-√(6))(√(3)-√(6)) )/((√(3)+√(6))(√(3)-√(6)) )` ← expand numerator/ denominator using FOIL

=
`(3-√(18)-√(18)+6 )/(3-√(18)+√(18)+6 )`

=
`(9-2√(18) )/(3+6)`

=
`(9-2(3√(2)) )/(9)`

=
`(9-6√(2) )/(9)`

=
`(9)/(9)` -
`(6√(2) )/(9)`

= 1 -
`(2√(2) )/(3)`