Solve sqrt{360}*sqrt{490}=

$$\sqrt { 360 } \cdot \sqrt { 490 } =$$

Evaluate

$$420$$

Solution Steps

Factor 360=6^{2}\times 10. Rewrite the square root of the product \sqrt{6^{2}\times 10} as the product of square roots \sqrt{6^{2}}\sqrt{10}. Take the square root of 6^{2}.

$$6\sqrt{10}\sqrt{490}$$

Factor 490=7^{2}\times 10. Rewrite the square root of the product \sqrt{7^{2}\times 10} as the product of square roots \sqrt{7^{2}}\sqrt{10}. Take the square root of 7^{2}.

$$6\sqrt{10}\times 7\sqrt{10}$$

Multiply 6 and 7 to get 42.

$$42\sqrt{10}\sqrt{10}$$

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

$$42\times 10$$

Multiply 42 and 10 to get 420.

$$420$$

Factor

$$2^{2}\times 3\times 5\times 7$$