Solve sqrt{2}(sqrt{6}+sqrt{10})

$$\sqrt{ 2 } ( \sqrt{ 6 } + \sqrt{ 10 } )$$

Evaluate

$$2\left(\sqrt{3}+\sqrt{5}\right)\approx 7.93623757$$

Solution Steps

Use the distributive property to multiply \sqrt{2} by \sqrt{6}+\sqrt{10}.

$$\sqrt{2}\sqrt{6}+\sqrt{2}\sqrt{10}$$

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

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

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

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

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}.

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

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

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