Solve 1+sqrt{31/3}

$$1+ \sqrt{ \frac{ 31 }{ 3 } }$$

Evaluate

$$\frac{\sqrt{93}}{3}+1\approx 4.214550254$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{31}{3}} as the division of square roots \frac{\sqrt{31}}{\sqrt{3}}.

$$1+\frac{\sqrt{31}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{31}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$1+\frac{\sqrt{31}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$1+\frac{\sqrt{31}\sqrt{3}}{3}$$

To multiply \sqrt{31} and \sqrt{3}, multiply the numbers under the square root.

$$1+\frac{\sqrt{93}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

$$\frac{3}{3}+\frac{\sqrt{93}}{3}$$

Since \frac{3}{3} and \frac{\sqrt{93}}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+\sqrt{93}}{3}$$