Solve frac{3sqrt{5}}{sqrt{7}}+2sqrt{2}

$$\frac{ 3 \sqrt{ 5 } }{ \sqrt{ 7 } } +2 \sqrt{ 2 }$$

Evaluate

$$\frac{3\sqrt{35}}{7}+2\sqrt{2}\approx 5.363889889$$

Short Solution Steps

Rationalize the denominator of \frac{3\sqrt{5}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{3\sqrt{5}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}+2\sqrt{2}$$

The square of \sqrt{7} is 7.

$$\frac{3\sqrt{5}\sqrt{7}}{7}+2\sqrt{2}$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{3\sqrt{35}}{7}+2\sqrt{2}$$

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

$$\frac{3\sqrt{35}}{7}+\frac{7\times 2\sqrt{2}}{7}$$

Since \frac{3\sqrt{35}}{7} and \frac{7\times 2\sqrt{2}}{7} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{35}+7\times 2\sqrt{2}}{7}$$

Do the multiplications in 3\sqrt{35}+7\times 2\sqrt{2}.

$$\frac{3\sqrt{35}+14\sqrt{2}}{7}$$