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

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

Evaluate

$$2\sqrt{5}+5\sqrt{2}\approx 11.543203767$$

Solution Steps

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

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

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}.

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

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

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

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}.

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

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

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