Solve sqrt{45}*sqrt{845}

$$\sqrt { 45 } \cdot \sqrt { 845 }$$

Evaluate

$$195$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$3\sqrt{5}\sqrt{845}$$

Factor 845=13^{2}\times 5. Rewrite the square root of the product \sqrt{13^{2}\times 5} as the product of square roots \sqrt{13^{2}}\sqrt{5}. Take the square root of 13^{2}.

$$3\sqrt{5}\times 13\sqrt{5}$$

Multiply 3 and 13 to get 39.

$$39\sqrt{5}\sqrt{5}$$

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

$$39\times 5$$

Multiply 39 and 5 to get 195.

$$195$$

Factor

$$3\times 5\times 13$$