Solve sqrt{1+2+3/6}

$$\sqrt{ 1+2+ \frac{ 3 }{ 6 } }$$

Evaluate

$$\frac{\sqrt{14}}{2}\approx 1.870828693$$

Solution Steps

Add 1 and 2 to get 3.

$$\sqrt{3+\frac{3}{6}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\sqrt{3+\frac{1}{2}}$$

Convert 3 to fraction \frac{6}{2}.

$$\sqrt{\frac{6}{2}+\frac{1}{2}}$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{6+1}{2}}$$

Add 6 and 1 to get 7.

$$\sqrt{\frac{7}{2}}$$

Rewrite the square root of the division \sqrt{\frac{7}{2}} as the division of square roots \frac{\sqrt{7}}{\sqrt{2}}.

$$\frac{\sqrt{7}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{7}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{7}\sqrt{2}}{2}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{14}}{2}$$