Solve sqrt{1+1/3}

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

Evaluate

$$\frac{2\sqrt{3}}{3}\approx 1.154700538$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add 3 and 1 to get 4.

$$\sqrt{\frac{4}{3}}$$

Rewrite the square root of the division \sqrt{\frac{4}{3}} as the division of square roots \frac{\sqrt{4}}{\sqrt{3}}.

$$\frac{\sqrt{4}}{\sqrt{3}}$$

Calculate the square root of 4 and get 2.

$$\frac{2}{\sqrt{3}}$$

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{3}}{3}$$