Question

How do you simplify `2 / (5 - sqrt 2)`?

Answer 1

`2/(5-sqrt(2)) = (10+2sqrt(2))/23`

Explanation:

We can rationalize the denominator by multiplying it (and the numerator) by the conjugate of the denominator.

`2/(5-sqrt(2))`
`color(white)("XXX")=2/(5-sqrt(2)) xx (5+sqrt(2))/(5+sqrt(2))`

`color(white)("XXX")=(10+2sqrt(2))/(5^2-(sqrt(2))^2)`

`color(white)("XXX")=(10+2sqrt(2))/23`

(Some people would consider this "simpler").