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

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

Evaluate

$$24\sqrt{3}\approx 41.569219382$$

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}.

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

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

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

Multiply 2 and 2 to get 4.

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

Multiply 4 and 3 to get 12.

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

Multiply 12 and 2 to get 24.

$$24\sqrt{3}$$