Solve 3sqrt{6}*2sqrt{2}*3sqrt{12}

$$3 \sqrt { 6 } \cdot 2 \sqrt { 2 } \cdot 3 \sqrt { 12 }$$

Evaluate

$$216$$

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}.

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

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

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

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}.

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

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

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

Multiply 2 and 3 to get 6.

$$6\times 3\times 2\times 3\sqrt{4}$$

Multiply 6 and 3 to get 18.

$$18\times 2\times 3\sqrt{4}$$

Multiply 18 and 2 to get 36.

$$36\times 3\sqrt{4}$$

Multiply 36 and 3 to get 108.

$$108\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$108\times 2$$

Multiply 108 and 2 to get 216.

$$216$$

Factor

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