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

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

Evaluate

$$12$$

Solution Steps

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}.

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

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

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

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

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

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

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

Multiply 2 and 3 to get 6.

$$6\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$6\times 2$$

Multiply 6 and 2 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$