Solve sqrt{1-36/133}

$$\sqrt { 1 - \frac { 36 } { 133 } }$$

Evaluate

$$\frac{\sqrt{12901}}{133}\approx 0.854004279$$

Solution Steps

Convert 1 to fraction \frac{133}{133}.

$$\sqrt{\frac{133}{133}-\frac{36}{133}}$$

Since \frac{133}{133} and \frac{36}{133} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{133-36}{133}}$$

Subtract 36 from 133 to get 97.

$$\sqrt{\frac{97}{133}}$$

Rewrite the square root of the division \sqrt{\frac{97}{133}} as the division of square roots \frac{\sqrt{97}}{\sqrt{133}}.

$$\frac{\sqrt{97}}{\sqrt{133}}$$

Rationalize the denominator of \frac{\sqrt{97}}{\sqrt{133}} by multiplying numerator and denominator by \sqrt{133}.

$$\frac{\sqrt{97}\sqrt{133}}{\left(\sqrt{133}\right)^{2}}$$

The square of \sqrt{133} is 133.

$$\frac{\sqrt{97}\sqrt{133}}{133}$$

To multiply \sqrt{97} and \sqrt{133}, multiply the numbers under the square root.

$$\frac{\sqrt{12901}}{133}$$