Solve frac{frac{sqrt{13}(frac{sqrt{2}}{2}+frac{sqrt{2}}{2}}{sqrt{3}}}{2}

$$\frac{ \frac{ \sqrt{ 13 } ( \frac{ \sqrt{ 2 } }{ 2 } + \frac{ \sqrt{ 2 } }{ 2 } }{ \sqrt{ 3 } } }{ 2 }$$

Evaluate

$$\frac{\sqrt{78}}{6}\approx 1.471960144$$

Solution Steps

Express \frac{\frac{\sqrt{13}\left(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\right)}{\sqrt{3}}}{2} as a single fraction.

$$\frac{\sqrt{13}\left(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\right)}{\sqrt{3}\times 2}$$

Combine \frac{\sqrt{2}}{2} and \frac{\sqrt{2}}{2} to get \sqrt{2}.

$$\frac{\sqrt{13}\sqrt{2}}{\sqrt{3}\times 2}$$

To multiply \sqrt{13} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{26}}{\sqrt{3}\times 2}$$

Rationalize the denominator of \frac{\sqrt{26}}{\sqrt{3}\times 2} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{26}\sqrt{3}}{\left(\sqrt{3}\right)^{2}\times 2}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{26}\sqrt{3}}{3\times 2}$$

To multiply \sqrt{26} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{78}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{78}}{6}$$