Solve 4sqrt{3}*6sqrt{20}*3sqrt{8}

$$4 \sqrt { 3 } \times 6 \sqrt { 20 } \times 3 \sqrt { 8 }$$

Evaluate

$$288\sqrt{30}\approx 1577.440965615$$

Solution Steps

Multiply 3 and 4 to get 12.

$$12\times 6\sqrt{3}\sqrt{20}\sqrt{8}$$

Multiply 12 and 6 to get 72.

$$72\sqrt{3}\sqrt{20}\sqrt{8}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$72\sqrt{3}\times 2\sqrt{5}\sqrt{8}$$

Multiply 72 and 2 to get 144.

$$144\sqrt{3}\sqrt{5}\sqrt{8}$$

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}.

$$144\sqrt{3}\sqrt{5}\times 2\sqrt{2}$$

Multiply 144 and 2 to get 288.

$$288\sqrt{3}\sqrt{5}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$288\sqrt{15}\sqrt{2}$$

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$288\sqrt{30}$$