Solve 2sqrt{8}*sqrt{125}*sqrt{40}

$$2 \sqrt { 8 } \times \sqrt { 125 } \times \sqrt { 40 }$$

Evaluate

$$400$$

Solution Steps

Factor 40=8\times 5. Rewrite the square root of the product \sqrt{8\times 5} as the product of square roots \sqrt{8}\sqrt{5}.

$$2\sqrt{8}\sqrt{125}\sqrt{8}\sqrt{5}$$

Multiply \sqrt{8} and \sqrt{8} to get 8.

$$2\times 8\sqrt{125}\sqrt{5}$$

Factor 125=5\times 25. Rewrite the square root of the product \sqrt{5\times 25} as the product of square roots \sqrt{5}\sqrt{25}.

$$2\times 8\sqrt{5}\sqrt{25}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$2\times 8\times 5\sqrt{25}$$

Multiply 2 and 8 to get 16.

$$16\times 5\sqrt{25}$$

Multiply 16 and 5 to get 80.

$$80\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$80\times 5$$

Multiply 80 and 5 to get 400.

$$400$$

Factor

$$2^{4}\times 5^{2}$$