Rationalize the denominator and simplify 6/√2-√3

=3 √6 - 3 √5

Explanation:

3 √5 + √6

We rationalise the denominator by multiplying the expression by the conjugate of the denominator. √5 - √6

3⋅ (√5 - √6) (√5 + √6) ⋅ (√5 - √6)

= 3⋅ (√5) + 3⋅ ( - √6) (√5 + √6) ⋅ (√5 - √6)

= 3 √5 - 3 √6 (√5 + √6) ⋅ (√5 - √6)

Applying identity

(a+b) (a-b) = a2 - b2 to the denominator.

= 3 √5 - 3 √6 (√5) 2 - (√6) 2

= 3 √5 - 3 √6 5-6

= 3 √5 - 3 √6 - 1

=-3 √5 + 3 √6

=3 √6 - 3 √ 5