Solve frac{sqrt{5-2}}{sqrt{6-1}}

$$\frac{ \sqrt{ 5-2 } }{ \sqrt{ 6-1 } }$$

Evaluate

$$\frac{\sqrt{15}}{5}\approx 0.774596669$$

Solution Steps

Subtract 2 from 5 to get 3.

$$\frac{\sqrt{3}}{\sqrt{6-1}}$$

Subtract 1 from 6 to get 5.

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

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

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

The square of \sqrt{5} is 5.

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

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

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