Solve sqrt{18}*sqrt{20}*sqrt{40}

$$\sqrt { 18 } \times \sqrt { 20 } \times \sqrt { 40 }$$

Evaluate

$$120$$

Solution Steps

Factor 40=20\times 2. Rewrite the square root of the product \sqrt{20\times 2} as the product of square roots \sqrt{20}\sqrt{2}.

$$\sqrt{18}\sqrt{20}\sqrt{20}\sqrt{2}$$

Multiply \sqrt{20} and \sqrt{20} to get 20.

$$\sqrt{18}\times 20\sqrt{2}$$

Factor 18=2\times 9. Rewrite the square root of the product \sqrt{2\times 9} as the product of square roots \sqrt{2}\sqrt{9}.

$$\sqrt{2}\sqrt{9}\times 20\sqrt{2}$$

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

$$2\times 20\sqrt{9}$$

Multiply 2 and 20 to get 40.

$$40\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$40\times 3$$

Multiply 40 and 3 to get 120.

$$120$$

Factor

$$2^{3}\times 3\times 5$$