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

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

Evaluate

$$\frac{\sqrt{14}+\sqrt{21}}{7}\approx 1.189176155$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}+\sqrt{3}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

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

The square of \sqrt{7} is 7.

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

Use the distributive property to multiply \sqrt{2}+\sqrt{3} by \sqrt{7}.

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

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

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

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{14}+\sqrt{21}}{7}$$