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

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

Evaluate

$$\sqrt{10}+2\sqrt{3}\approx 6.626379275$$

Solution Steps

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

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

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

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

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}.

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

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

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