Solve sqrt{115/6}

$$\sqrt { 11 \frac { 5 } { 6 } }$$

Evaluate

$$\frac{\sqrt{426}}{6}\approx 3.43996124$$

Solution Steps

Multiply 11 and 6 to get 66.

$$\sqrt{\frac{66+5}{6}}$$

Add 66 and 5 to get 71.

$$\sqrt{\frac{71}{6}}$$

Rewrite the square root of the division \sqrt{\frac{71}{6}} as the division of square roots \frac{\sqrt{71}}{\sqrt{6}}.

$$\frac{\sqrt{71}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{71}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{71}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{71}\sqrt{6}}{6}$$

To multiply \sqrt{71} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{426}}{6}$$