Answer
True
Work Step by Step
We simplify the equation by rationalizing its denominator. To rationalize the denominator, we multiply both the numerator and the denominator by $\sqrt 2$:
$\frac{\sqrt 8+\sqrt {12}}{\sqrt 2}\times\frac{\sqrt 2}{\sqrt 2}$
=$\frac{\sqrt 2(\sqrt 8+\sqrt {12})}{\sqrt 2\times\sqrt 2}$
=$\frac{\sqrt 2\sqrt 8+\sqrt 2\sqrt {12}}{2}$
=$\frac{\sqrt {2\times8}+\sqrt {2\times12}}{2}$
=$\frac{\sqrt {16}+\sqrt {24}}{2}$
=$\frac{4+\sqrt {4\times6}}{2}$
=$\frac{4+2\sqrt {6}}{2}$
=$2+\sqrt {6}$
Therefore, the question statement is true.
