Solve frac{(sqrt{7}+sqrt{13})}{sqrt{15}}

$$\frac { ( \sqrt { 7 } + \sqrt { 13 } ) } { \sqrt { 15 } }$$

Evaluate

$$\frac{\sqrt{105}+\sqrt{195}}{15}\approx 1.614079387$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{7}+\sqrt{13}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\left(\sqrt{7}+\sqrt{13}\right)\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\left(\sqrt{7}+\sqrt{13}\right)\sqrt{15}}{15}$$

Use the distributive property to multiply \sqrt{7}+\sqrt{13} by \sqrt{15}.

$$\frac{\sqrt{7}\sqrt{15}+\sqrt{13}\sqrt{15}}{15}$$

To multiply \sqrt{7} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{105}+\sqrt{13}\sqrt{15}}{15}$$

To multiply \sqrt{13} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{105}+\sqrt{195}}{15}$$