Question

How do you rationalize the denominator and simplify: `2 / (5 - sqrt 2)`?

Answer 1

To rationalize, multiply the numerator and the denominator by the conjugate of 5-`sqrt2`. This is 5+`sqrt2`.

Accordingly it is 2(5+`sqrt2`)/(5-`sqrt2`)(5+`sqrt2`)
= 2(5+`sqrt2`)/(25-2)
= `2/23` (5+`sqrt2`)