Solve sqrt{2}(3+2sqrt{6})

$$\sqrt{ 2 } (3+2 \sqrt{ 6 } )$$

Evaluate

$$\sqrt{3}\left(\sqrt{6}+4\right)\approx 11.170843917$$

Solution Steps

Use the distributive property to multiply \sqrt{2} by 3+2\sqrt{6}.

$$3\sqrt{2}+2\sqrt{2}\sqrt{6}$$

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}.

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

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

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

Multiply 2 and 2 to get 4.

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