Solve =frac{sqrt{45}*sqrt{32}}{sqrt{360}}

$$= \frac { \sqrt { 45 } \times \sqrt { 32 } } { \sqrt { 360 } }$$

Evaluate

$$2$$

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}.

$$\frac{3\sqrt{5}\sqrt{32}}{\sqrt{360}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{3\sqrt{5}\times 4\sqrt{2}}{\sqrt{360}}$$

Multiply 3 and 4 to get 12.

$$\frac{12\sqrt{5}\sqrt{2}}{\sqrt{360}}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{12\sqrt{10}}{\sqrt{360}}$$

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}.

$$\frac{12\sqrt{10}}{6\sqrt{10}}$$

Cancel out 6\sqrt{10} in both numerator and denominator.

$$2$$

Factor

$$2$$