Solve sqrt{3}sqrt{8}sqrt{6}=

$$\sqrt { 3 } \sqrt { 8 } \sqrt { 6 } =$$

Evaluate

$$12$$

Solution Steps

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}.

$$\sqrt{3}\sqrt{8}\sqrt{3}\sqrt{2}$$

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

$$3\sqrt{8}\sqrt{2}$$

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}.

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

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

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

Multiply 3 and 2 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

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