Question

Rationalize the denominator

11/Square root of 5 - square root of 6

Answer 1

`-11√(5)-11√(6)`

Explanation:

The given radical expression is;

`(11)/(√(5)-√(6))`

We multiply both the numerator and the denominator by the conjugate of

`√(5)-√(6)` which is
`√(5)+√(6)`

`(11(√(5)+√(6)))/((√(5)-√(6))(√(5)+√(6)))`

The denominator is now difference of two squares;

`(11(√(5)+√(6)))/((√(5))^2-(√(6))^2)`

Simplify:

`(11(√(5)+√(6)))/(5-6)`

`(11(√(5)+√(6)))/(-1)`

`-11(√(5)+√(6))`

`-11√(5)-11√(6)`