Solve 6/sqrt{7}+8/sqrt{2}

$$\frac { 6 } { \sqrt { 7 } } + \frac { 8 } { \sqrt { 2 } }$$

Evaluate

$$\frac{6\sqrt{7}}{7}+4\sqrt{2}\approx 7.924641088$$

Short Solution Steps

Rationalize the denominator of \frac{6}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{6\sqrt{7}}{\left(\sqrt{7}\right)^{2}}+\frac{8}{\sqrt{2}}$$

The square of \sqrt{7} is 7.

$$\frac{6\sqrt{7}}{7}+\frac{8}{\sqrt{2}}$$

Rationalize the denominator of \frac{8}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{6\sqrt{7}}{7}+\frac{8\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{6\sqrt{7}}{7}+\frac{8\sqrt{2}}{2}$$

Divide 8\sqrt{2} by 2 to get 4\sqrt{2}.

$$\frac{6\sqrt{7}}{7}+4\sqrt{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4\sqrt{2} times \frac{7}{7}.

$$\frac{6\sqrt{7}}{7}+\frac{7\times 4\sqrt{2}}{7}$$

Since \frac{6\sqrt{7}}{7} and \frac{7\times 4\sqrt{2}}{7} have the same denominator, add them by adding their numerators.

$$\frac{6\sqrt{7}+7\times 4\sqrt{2}}{7}$$

Do the multiplications in 6\sqrt{7}+7\times 4\sqrt{2}.

$$\frac{6\sqrt{7}+28\sqrt{2}}{7}$$

Factor

$$\frac{2 {(3 \sqrt{7} + 14 \sqrt{2})}}{7} = 7.9246410875477435$$