Solve 5sqrt{3}*(sqrt{2}+sqrt{6})

$$5 \sqrt{ 3 } \times ( \sqrt{ 2 } + \sqrt{ 6 } )$$

Evaluate

$$5\left(\sqrt{6}+3\sqrt{2}\right)\approx 33.46065215$$

Solution Steps

Use the distributive property to multiply 5\sqrt{3} by \sqrt{2}+\sqrt{6}.

$$5\sqrt{3}\sqrt{2}+5\sqrt{3}\sqrt{6}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$5\sqrt{6}+5\sqrt{3}\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$5\sqrt{6}+5\sqrt{3}\sqrt{3}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$5\sqrt{6}+5\times 3\sqrt{2}$$

Multiply 5 and 3 to get 15.

$$5\sqrt{6}+15\sqrt{2}$$