Solve sqrt{90}*sqrt{40}60

$$\sqrt { 90 } \cdot \sqrt { 40 } 60$$

Evaluate

$$3600$$

Solution Steps

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$60\times 3\sqrt{10}\sqrt{40}$$

Multiply 60 and 3 to get 180.

$$180\sqrt{10}\sqrt{40}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$180\sqrt{10}\times 2\sqrt{10}$$

Multiply 180 and 2 to get 360.

$$360\sqrt{10}\sqrt{10}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$360\times 10$$

Multiply 360 and 10 to get 3600.

$$3600$$

Factor

$$2^{4}\times 3^{2}\times 5^{2}$$