Solve sqrt{18*80}*sqrt{2}*sqrt{5}

$$\sqrt { 18 \cdot 80 } \cdot \sqrt { 2 } \cdot \sqrt { 5 }$$

Evaluate

$$120$$

Solution Steps

Multiply 18 and 80 to get 1440.

$$\sqrt{1440}\sqrt{2}\sqrt{5}$$

Factor 1440=12^{2}\times 10. Rewrite the square root of the product \sqrt{12^{2}\times 10} as the product of square roots \sqrt{12^{2}}\sqrt{10}. Take the square root of 12^{2}.

$$12\sqrt{10}\sqrt{2}\sqrt{5}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$12\sqrt{2}\sqrt{5}\sqrt{2}\sqrt{5}$$

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

$$12\times 2\sqrt{5}\sqrt{5}$$

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

$$12\times 2\times 5$$

Multiply 12 and 2 to get 24.

$$24\times 5$$

Multiply 24 and 5 to get 120.

$$120$$

Factor

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