Question

rationalize the denominator of the following expression and simplify: sqrt 3 - sqrt 6/ sqrt 3 + sqrt 6

Answer 1

-3 + 2√2. Option B is correct

Explanations:

Given the surd function expressed as:

`(√(3)-√(6))/(√(3)+√(6))`

Rationalise the denominator

`\begin{gathered} =(√(3)-√(6))/(√(3)+√(6))*(√(3)-√(6))/(√(3)-√(6)) \\ =(3-√(18)-√(18)+6)/(3-6) \\ =(3-2√(18)+6)/(-3) \\ =(9-2√(18))/(-3) \\ =(9-2(3√(2)))/(-3) \\ =-3+2√(2) \end{gathered}`

Hence the simplified form of the expression is -3 + 2√2