Solve sqrt{45}*sqrt{605}

$$\sqrt{ 45 } \times \sqrt{ 605 }$$

Evaluate

$$165$$

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}.

$$3\sqrt{5}\sqrt{605}$$

Factor 605=11^{2}\times 5. Rewrite the square root of the product \sqrt{11^{2}\times 5} as the product of square roots \sqrt{11^{2}}\sqrt{5}. Take the square root of 11^{2}.

$$3\sqrt{5}\times 11\sqrt{5}$$

Multiply 3 and 11 to get 33.

$$33\sqrt{5}\sqrt{5}$$

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

$$33\times 5$$

Multiply 33 and 5 to get 165.

$$165$$

Factor

$$3\times 5\times 11$$