Solve sqrt{6}*(sqrt{30}+sqrt{10})=

$$\sqrt { 6 } \cdot ( \sqrt { 30 } + \sqrt { 10 } ) =$$

Evaluate

$$2\left(\sqrt{15}+3\sqrt{5}\right)\approx 21.162374557$$

Solution Steps

Use the distributive property to multiply \sqrt{6} by \sqrt{30}+\sqrt{10}.

$$\sqrt{6}\sqrt{30}+\sqrt{6}\sqrt{10}$$

Factor 30=6\times 5. Rewrite the square root of the product \sqrt{6\times 5} as the product of square roots \sqrt{6}\sqrt{5}.

$$\sqrt{6}\sqrt{6}\sqrt{5}+\sqrt{6}\sqrt{10}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$6\sqrt{5}+\sqrt{6}\sqrt{10}$$

To multiply \sqrt{6} and \sqrt{10}, multiply the numbers under the square root.

$$6\sqrt{5}+\sqrt{60}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

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