Solve 9/7+sqrt{7/2}

$$\frac{ 9 }{ 7 } + \sqrt{ \frac{ 7 }{ 2 } }$$

Evaluate

$$\frac{\sqrt{14}}{2}+\frac{9}{7}\approx 3.156542979$$

Short Solution Steps

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

$$\frac{9}{7}+\frac{\sqrt{7}}{\sqrt{2}}$$

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

$$\frac{9}{7}+\frac{\sqrt{7}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{9}{7}+\frac{\sqrt{7}\sqrt{2}}{2}$$

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

$$\frac{9}{7}+\frac{\sqrt{14}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 2 is 14. Multiply \frac{9}{7} times \frac{2}{2}. Multiply \frac{\sqrt{14}}{2} times \frac{7}{7}.

$$\frac{9\times 2}{14}+\frac{7\sqrt{14}}{14}$$

Since \frac{9\times 2}{14} and \frac{7\sqrt{14}}{14} have the same denominator, add them by adding their numerators.

$$\frac{9\times 2+7\sqrt{14}}{14}$$

Do the multiplications in 9\times 2+7\sqrt{14}.

$$\frac{18+7\sqrt{14}}{14}$$

Factor

$$\frac{7 \sqrt{14} + 18}{14} = 3.1565429791012565$$