Question

How do you simplify `9/(6-sqrt8)`?

Answer 1

Multiply the top and bottom by `(6 + sqrt8)` to make a difference of two squares and remove the square root.

Explanation:

The difference of two squares:
`(a + b)(a -b) = a^2 - ab + ab -b^2 = a^2 - b^2`

`= (9(6+sqrt8))/((6-sqrt8)(6+sqrt8))`

`=(54+9sqrt8)/(6^2 - (sqrt8)^2)`

`=(54+9sqrt8)/(36-8)`

`=(54+9sqrt8)/28`

This is now simplified, as a fraction can have a root on top, but not on the bottom (as then it is irrational).

You could also round this value to 2.84, but the answer calculated is exact.