Solve sqrt{6}sqrt{8}sqrt{12}=

$$\sqrt { 6 } \sqrt { 8 } \sqrt { 12 } =$$

Evaluate

$$24$$

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}.

$$\sqrt{6}\sqrt{8}\sqrt{6}\sqrt{2}$$

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

$$6\sqrt{8}\sqrt{2}$$

Factor 8=2\times 4. Rewrite the square root of the product \sqrt{2\times 4} as the product of square roots \sqrt{2}\sqrt{4}.

$$6\sqrt{2}\sqrt{4}\sqrt{2}$$

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

$$6\times 2\sqrt{4}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$12\times 2$$

Multiply 12 and 2 to get 24.

$$24$$

Factor

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