Solve 2sqrt{2}*2sqrt{3}*2sqrt{6}*3sqrt{8}

$$2 \sqrt{ 2 } \times 2 \sqrt{ 3 } \times 2 \sqrt{ 6 } \times 3 \sqrt{ 8 }$$

Evaluate

$$288\sqrt{2}\approx 407.293505963$$

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}.

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

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

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

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

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

Multiply 2 and 2 to get 4.

$$4\times 2\times 3\times 2\times 3\sqrt{8}$$

Multiply 4 and 2 to get 8.

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

Multiply 8 and 3 to get 24.

$$24\times 2\times 3\sqrt{8}$$

Multiply 24 and 2 to get 48.

$$48\times 3\sqrt{8}$$

Multiply 48 and 3 to get 144.

$$144\sqrt{8}$$

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

$$144\times 2\sqrt{2}$$

Multiply 144 and 2 to get 288.

$$288\sqrt{2}$$