Solve frac{sqrt{36}}{sqrt{45}}

$$\frac { \sqrt { 36 } } { \sqrt { 45 } }$$

Evaluate

$$\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Solution Steps

Calculate the square root of 36 and get 6.

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

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}.

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

Rationalize the denominator of \frac{6}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{6\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

Cancel out 3 in both numerator and denominator.

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