What is the simplest form of expression?

sqrt 3 - sqrt 6

over

sqrt 3 + sqrt 6

It's in a decimal form

(√3-√6) / (√3+√6)

We have to multiply the denominator and numerator by the conjugate of the denominator.

the conjugate of the denominator is : (√3-√6)

Therefore:

(√3-√6) / (√3+√6) = [ (√3-√6) (√3-√6) ] / [ (√3+√6) (√3-√6) ]

= (√3-√6) ² / (3-6)

=[3-2 (√3) (√6) + 6] / - 3

= (9-2√18) / - 3

= (-9+6√2) / 3

=-3+2√2

Answer: (√3-√6) / (√3+√6) = - 3+2√2