Question

What is the conjugate?
Sqrt 8 - sqrt 9

Answer 1

The conjugate of an irrational number is the number you have to multiply it by in order to arrive at a rational number.

Answer 2

`(-1)/((√(8)+√(9)))`

Explanation:

We are given the expression
`√(8)-√(9)`.

So, the conjugate is given by,

`(√(8)-√(9))* ((√(8)+√(9)))/((√(8)+√(9)))`

i.e.
`((√(8))^(2)-(√(9))^(2))/((√(8)+√(9)))`

i.e.
`(8-9)/((√(8)+√(9)))`

i.e.
`(-1)/((√(8)+√(9)))`

Thus, the conjugate of the expression is given by
`(-1)/((√(8)+√(9)))`.