Solve frac{sqrt{81}*sqrt{175}}{sqrt{1125}}

$$\frac { \sqrt { 81 } \times \sqrt { 175 } } { \sqrt { 1125 } }$$

Evaluate

$$\frac{3\sqrt{35}}{5}\approx 3.54964787$$

Solution Steps

Calculate the square root of 81 and get 9.

$$\frac{9\sqrt{175}}{\sqrt{1125}}$$

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$\frac{9\times 5\sqrt{7}}{\sqrt{1125}}$$

Multiply 9 and 5 to get 45.

$$\frac{45\sqrt{7}}{\sqrt{1125}}$$

Factor 1125=15^{2}\times 5. Rewrite the square root of the product \sqrt{15^{2}\times 5} as the product of square roots \sqrt{15^{2}}\sqrt{5}. Take the square root of 15^{2}.

$$\frac{45\sqrt{7}}{15\sqrt{5}}$$

Cancel out 15 in both numerator and denominator.

$$\frac{3\sqrt{7}}{\sqrt{5}}$$

Rationalize the denominator of \frac{3\sqrt{7}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{7}\sqrt{5}}{5}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{3\sqrt{35}}{5}$$