Solve sqrt{7+1/6}

$$\sqrt { 7 + \frac { 1 } { 6 } }$$

Evaluate

$$\frac{\sqrt{258}}{6}\approx 2.677063067$$

Solution Steps

Convert 7 to fraction \frac{42}{6}.

$$\sqrt{\frac{42}{6}+\frac{1}{6}}$$

Since \frac{42}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{42+1}{6}}$$

Add 42 and 1 to get 43.

$$\sqrt{\frac{43}{6}}$$

Rewrite the square root of the division \sqrt{\frac{43}{6}} as the division of square roots \frac{\sqrt{43}}{\sqrt{6}}.

$$\frac{\sqrt{43}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{43}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{43}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{43}\sqrt{6}}{6}$$

To multiply \sqrt{43} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{258}}{6}$$