Solve frac{sqrt{54}}{sqrt{45}}

$$\frac { \sqrt { 54 } } { \sqrt { 45 } }$$

Evaluate

$$\frac{\sqrt{30}}{5}\approx 1.095445115$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\frac{3\sqrt{6}}{\sqrt{45}}$$

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}.

$$\frac{3\sqrt{6}}{3\sqrt{5}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{6}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{6}\sqrt{5}}{5}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{5}$$