Question

(6+√25)/(4-√3) can be written in the form of (2+s√3)/13 where r and s are both integers what are the values of r and s

Answer 1

r = 33

s = 18

Explanation:

Given expression is
`(6+√(27))/(4-√(3))`.

Multiply numerator and denominator with the conjugate of (4 - √3).

`((6+√(27))(4+√(3)))/((4-√(3))(4+√(3)))`

=
`(4(6+√(27))+√(3)(6+√(27)))/(4^(2)-(√(3))^2)`

=
`(24+4√(27)+6√(3)+√(81)))/(16-3)`

=
`(24+12√(3)+6√(3)+√(81)))/(16-3)`

=
`(24+18√(3)+9)/(13)`

=
`(33+18√(3))/(13)`

Now compare this expression with
`(r+s√(3) )/(13)`

r = 33

s = 18