Solve sqrt{6}(sqrt{12}+2sqrt{6})

$$\sqrt { 6 } ( \sqrt { 12 } + 2 \sqrt { 6 } )$$

Evaluate

$$6\sqrt{2}+12\approx 20.485281374$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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

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

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}.

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

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

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

Multiply 2 and 3 to get 6.

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

The square of \sqrt{6} is 6.

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

Multiply 2 and 6 to get 12.

$$6\sqrt{2}+12$$