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

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

Evaluate

$$-\left(\sqrt{10}+2\sqrt{3}\right)\approx -6.626379275$$

Solution Steps

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

$$\left(-\sqrt{2}\right)\sqrt{5}+\left(-\sqrt{2}\right)\sqrt{6}$$

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.

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