Solve sqrt{10}(sqrt{5}+3sqrt{2})

$$\sqrt { 10 } ( \sqrt { 5 } + 3 \sqrt { 2 } )$$

Evaluate

$$\sqrt{5}\left(\sqrt{10}+6\right)\approx 20.487475677$$

Solution Steps

Use the distributive property to multiply \sqrt{10} by \sqrt{5}+3\sqrt{2}.

$$\sqrt{10}\sqrt{5}+3\sqrt{10}\sqrt{2}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\sqrt{5}\sqrt{2}\sqrt{5}+3\sqrt{10}\sqrt{2}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$5\sqrt{2}+3\sqrt{10}\sqrt{2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 3 and 2 to get 6.

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