Solve 17+sqrt{277div6}

$$17+ \sqrt{ 277 \div 6 }$$

Evaluate

$$\frac{\sqrt{1662}}{6}+17\approx 23.794605704$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{277}{6}} as the division of square roots \frac{\sqrt{277}}{\sqrt{6}}.

$$17+\frac{\sqrt{277}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{277}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$17+\frac{\sqrt{277}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$17+\frac{\sqrt{277}\sqrt{6}}{6}$$

To multiply \sqrt{277} and \sqrt{6}, multiply the numbers under the square root.

$$17+\frac{\sqrt{1662}}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 17 times \frac{6}{6}.

$$\frac{17\times 6}{6}+\frac{\sqrt{1662}}{6}$$

Since \frac{17\times 6}{6} and \frac{\sqrt{1662}}{6} have the same denominator, add them by adding their numerators.

$$\frac{17\times 6+\sqrt{1662}}{6}$$

Do the multiplications in 17\times 6+\sqrt{1662}.

$$\frac{102+\sqrt{1662}}{6}$$