Solve frac{4+5sqrt{2}}{sqrt{7}}

$$\frac { 4 + 5 \sqrt { 2 } } { \sqrt { 7 } }$$

Evaluate

$$\frac{4\sqrt{7}+5\sqrt{14}}{7}\approx 4.184470311$$

Solution Steps

Rationalize the denominator of \frac{4+5\sqrt{2}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\left(4+5\sqrt{2}\right)\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\left(4+5\sqrt{2}\right)\sqrt{7}}{7}$$

Use the distributive property to multiply 4+5\sqrt{2} by \sqrt{7}.

$$\frac{4\sqrt{7}+5\sqrt{2}\sqrt{7}}{7}$$

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

$$\frac{4\sqrt{7}+5\sqrt{14}}{7}$$