Solve sqrt{904}*sqrt{404}=

$$\sqrt { 904 } \times \sqrt { 404 } =$$

Evaluate

$$4\sqrt{22826}\approx 604.331035112$$

Solution Steps

Factor 904=2^{2}\times 226. Rewrite the square root of the product \sqrt{2^{2}\times 226} as the product of square roots \sqrt{2^{2}}\sqrt{226}. Take the square root of 2^{2}.

$$2\sqrt{226}\sqrt{404}$$

Factor 404=2^{2}\times 101. Rewrite the square root of the product \sqrt{2^{2}\times 101} as the product of square roots \sqrt{2^{2}}\sqrt{101}. Take the square root of 2^{2}.

$$2\sqrt{226}\times 2\sqrt{101}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{226}\sqrt{101}$$

To multiply \sqrt{226} and \sqrt{101}, multiply the numbers under the square root.

$$4\sqrt{22826}$$