Solve frac{frac{sqrt{26}}{2}+frac{sqrt{26}}{13}}{5/2sqrt{2}}

$$\frac { \frac { \sqrt { 26 } } { 2 } + \frac { \sqrt { 26 } } { 13 } } { \frac { 5 } { 2 } \sqrt { 2 } }$$

Evaluate

$$\frac{3\sqrt{13}}{13}\approx 0.832050294$$

Solution Steps

Combine \frac{\sqrt{26}}{2} and \frac{\sqrt{26}}{13} to get \frac{15}{26}\sqrt{26}.

$$\frac{\frac{15}{26}\sqrt{26}}{\frac{5}{2}\sqrt{2}}$$

Rationalize the denominator of \frac{\frac{15}{26}\sqrt{26}}{\frac{5}{2}\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{15}{26}\sqrt{26}\sqrt{2}}{\frac{5}{2}\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{15}{26}\sqrt{26}\sqrt{2}}{\frac{5}{2}\times 2}$$

Factor 26=2\times 13. Rewrite the square root of the product \sqrt{2\times 13} as the product of square roots \sqrt{2}\sqrt{13}.

$$\frac{\frac{15}{26}\sqrt{2}\sqrt{13}\sqrt{2}}{\frac{5}{2}\times 2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{\frac{15}{26}\times 2\sqrt{13}}{\frac{5}{2}\times 2}$$

Cancel out 2 and 2.

$$\frac{\frac{15}{26}\times 2\sqrt{13}}{5}$$

Express \frac{15}{26}\times 2 as a single fraction.

$$\frac{\frac{15\times 2}{26}\sqrt{13}}{5}$$

Multiply 15 and 2 to get 30.

$$\frac{\frac{30}{26}\sqrt{13}}{5}$$

Reduce the fraction \frac{30}{26} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{15}{13}\sqrt{13}}{5}$$

Divide \frac{15}{13}\sqrt{13} by 5 to get \frac{3}{13}\sqrt{13}.

$$\frac{3}{13}\sqrt{13}$$