Solve sqrt{6}*sqrt{12}sqrt{6*2}

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

Evaluate

$$12\sqrt{6}\approx 29.393876913$$

Solution Steps

Factor 12=6\times 2. Rewrite the square root of the product \sqrt{6\times 2} as the product of square roots \sqrt{6}\sqrt{2}.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

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

Multiply 6 and 2 to get 12.

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

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}.

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

Multiply 6 and 2 to get 12.

$$12\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$12\sqrt{6}$$