Solve frac{sqrt{23}-23}{sqrt{23}}=

$$\frac { \sqrt { 23 } - 23 } { \sqrt { 23 } } =$$

Evaluate

$$1-\sqrt{23}\approx -3.795831523$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{23}-23}{\sqrt{23}} by multiplying numerator and denominator by \sqrt{23}.

$$\frac{\left(\sqrt{23}-23\right)\sqrt{23}}{\left(\sqrt{23}\right)^{2}}$$

The square of \sqrt{23} is 23.

$$\frac{\left(\sqrt{23}-23\right)\sqrt{23}}{23}$$

Use the distributive property to multiply \sqrt{23}-23 by \sqrt{23}.

$$\frac{\left(\sqrt{23}\right)^{2}-23\sqrt{23}}{23}$$

The square of \sqrt{23} is 23.

$$\frac{23-23\sqrt{23}}{23}$$

Divide each term of 23-23\sqrt{23} by 23 to get 1-\sqrt{23}.

$$1-\sqrt{23}$$