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

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

Evaluate

$$6\left(\sqrt{2}+1\right)\approx 14.485281374$$

Solution Steps

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

$$2\sqrt{6}\sqrt{3}+\left(\sqrt{6}\right)^{2}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$2\sqrt{3}\sqrt{2}\sqrt{3}+\left(\sqrt{6}\right)^{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\times 3\sqrt{2}+\left(\sqrt{6}\right)^{2}$$

Multiply 2 and 3 to get 6.

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

The square of \sqrt{6} is 6.

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