Solve frac{sqrt{2}}{7}+frac{sqrt{8723}}{sqrt{23}}

$$\frac { \sqrt { 2 } } { 7 } + \frac { \sqrt { 8723 } } { \sqrt { 23 } }$$

Evaluate

$$\frac{\sqrt{2}}{7}+\frac{\sqrt{200629}}{23}\approx 19.676651675$$

Short Solution Steps

Rationalize the denominator of \frac{\sqrt{8723}}{\sqrt{23}} by multiplying numerator and denominator by \sqrt{23}.

$$\frac{\sqrt{2}}{7}+\frac{\sqrt{8723}\sqrt{23}}{\left(\sqrt{23}\right)^{2}}$$

The square of \sqrt{23} is 23.

$$\frac{\sqrt{2}}{7}+\frac{\sqrt{8723}\sqrt{23}}{23}$$

To multiply \sqrt{8723} and \sqrt{23}, multiply the numbers under the square root.

$$\frac{\sqrt{2}}{7}+\frac{\sqrt{200629}}{23}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 23 is 161. Multiply \frac{\sqrt{2}}{7} times \frac{23}{23}. Multiply \frac{\sqrt{200629}}{23} times \frac{7}{7}.

$$\frac{23\sqrt{2}}{161}+\frac{7\sqrt{200629}}{161}$$

Since \frac{23\sqrt{2}}{161} and \frac{7\sqrt{200629}}{161} have the same denominator, add them by adding their numerators.

$$\frac{23\sqrt{2}+7\sqrt{200629}}{161}$$

Factor

$$\frac{7 \sqrt{200629} + 23 \sqrt{2}}{161} = 19.676651675064544$$