Solve 5x+sqrt{5div6}

$$5x+ \sqrt{ 5 \div 6 }$$

Evaluate

$$5x+\frac{\sqrt{30}}{6}$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{6}} as the division of square roots \frac{\sqrt{5}}{\sqrt{6}}.

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

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$5x+\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$5x+\frac{\sqrt{30}}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x times \frac{6}{6}.

$$\frac{6\times 5x}{6}+\frac{\sqrt{30}}{6}$$

Since \frac{6\times 5x}{6} and \frac{\sqrt{30}}{6} have the same denominator, add them by adding their numerators.

$$\frac{6\times 5x+\sqrt{30}}{6}$$

Do the multiplications in 6\times 5x+\sqrt{30}.

$$\frac{30x+\sqrt{30}}{6}$$

Differentiate w.r.t. x

$$5$$