Solve sqrt{9-81/61}

$$\sqrt { 9 - \frac { 81 } { 61 } }$$

Evaluate

$$\frac{6\sqrt{793}}{61}\approx 2.769861214$$

Solution Steps

Convert 9 to fraction \frac{549}{61}.

$$\sqrt{\frac{549}{61}-\frac{81}{61}}$$

Since \frac{549}{61} and \frac{81}{61} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{549-81}{61}}$$

Subtract 81 from 549 to get 468.

$$\sqrt{\frac{468}{61}}$$

Rewrite the square root of the division \sqrt{\frac{468}{61}} as the division of square roots \frac{\sqrt{468}}{\sqrt{61}}.

$$\frac{\sqrt{468}}{\sqrt{61}}$$

Factor 468=6^{2}\times 13. Rewrite the square root of the product \sqrt{6^{2}\times 13} as the product of square roots \sqrt{6^{2}}\sqrt{13}. Take the square root of 6^{2}.

$$\frac{6\sqrt{13}}{\sqrt{61}}$$

Rationalize the denominator of \frac{6\sqrt{13}}{\sqrt{61}} by multiplying numerator and denominator by \sqrt{61}.

$$\frac{6\sqrt{13}\sqrt{61}}{\left(\sqrt{61}\right)^{2}}$$

The square of \sqrt{61} is 61.

$$\frac{6\sqrt{13}\sqrt{61}}{61}$$

To multiply \sqrt{13} and \sqrt{61}, multiply the numbers under the square root.

$$\frac{6\sqrt{793}}{61}$$