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

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

Evaluate

$$144$$

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}.

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

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

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

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

$$2\times 2\times 6\times 3\times 2$$

Multiply 2 and 2 to get 4.

$$4\times 6\times 3\times 2$$

Multiply 4 and 6 to get 24.

$$24\times 3\times 2$$

Multiply 24 and 3 to get 72.

$$72\times 2$$

Multiply 72 and 2 to get 144.

$$144$$

Factor

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