Solve frac{77-sqrt{77}}{sqrt{77}}

$$\frac { 77 - \sqrt { 77 } } { \sqrt { 77 } }$$

Evaluate

$$\sqrt{77}-1\approx 7.774964387$$

Solution Steps

Rationalize the denominator of \frac{77-\sqrt{77}}{\sqrt{77}} by multiplying numerator and denominator by \sqrt{77}.

$$\frac{\left(77-\sqrt{77}\right)\sqrt{77}}{\left(\sqrt{77}\right)^{2}}$$

The square of \sqrt{77} is 77.

$$\frac{\left(77-\sqrt{77}\right)\sqrt{77}}{77}$$

Use the distributive property to multiply 77-\sqrt{77} by \sqrt{77}.

$$\frac{77\sqrt{77}-\left(\sqrt{77}\right)^{2}}{77}$$

The square of \sqrt{77} is 77.

$$\frac{77\sqrt{77}-77}{77}$$

Divide each term of 77\sqrt{77}-77 by 77 to get \sqrt{77}-1.

$$\sqrt{77}-1$$

Factor

$$\sqrt{77} - 1 = 7.774964387$$