Solve sqrt{2}(4+sqrt{6})

$$\sqrt { 2 } ( 4 + \sqrt { 6 } )$$

Evaluate

$$2\left(\sqrt{3}+2\sqrt{2}\right)\approx 9.120955865$$

Solution Steps

Use the distributive property to multiply \sqrt{2} by 4+\sqrt{6}.

$$4\sqrt{2}+\sqrt{2}\sqrt{6}$$

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}.

$$4\sqrt{2}+\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$4\sqrt{2}+2\sqrt{3}$$