Question

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

Answer 1

Answer:

-3 + 2√2. Option B is correct

Explanations:

Given the surd function expressed as:

$\frac{\sqrt{3}-\sqrt{6}}{\sqrt{3}+\sqrt{6}}$

Rationalise the denominator

$\begin{gathered} =\frac{\sqrt{3}-\sqrt{6}}{\sqrt{3}+\sqrt{6}}\times\frac{\sqrt{3}-\sqrt{6}}{\sqrt{3}-\sqrt{6}} \\ =\frac{3-\sqrt{18}-\sqrt{18}+6}{3-6} \\ =\frac{3-2\sqrt{18}+6}{-3} \\ =\frac{9-2\sqrt{18}}{-3} \\ =\frac{9-2(3\sqrt{2})}{-3} \\ =-3+2\sqrt{2} \end{gathered}$

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