Fully simplify sqrt(54) + sqrt(24)sqrt(2)

Find the largest perfect square factors for 54 and 24.
For $\sqrt{54}$: $54 = 9 \times 6$.

$$\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6}$$

For $\sqrt{24}$: $24 = 4 \times 6$.

$$\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}$$

$$\frac{5\sqrt{6}}{\sqrt{2}}$$

Use the property $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$.

$$5\sqrt{\frac{6}{2}} = 5\sqrt{3}$$

The fully simplified expression is:

$$5\sqrt{3}$$