Solve frac{frac{3sqrt{17}}{14}}{frac{45sqrt{7}}{14}}

$$\frac { \frac { 3 \sqrt { 17 } } { 14 } } { \frac { 45 \sqrt { 7 } } { 14 } }$$

Evaluate

$$\frac{\sqrt{119}}{105}\approx 0.103892496$$

Solution Steps

Divide \frac{3\sqrt{17}}{14} by \frac{45\sqrt{7}}{14} by multiplying \frac{3\sqrt{17}}{14} by the reciprocal of \frac{45\sqrt{7}}{14}.

$$\frac{3\sqrt{17}\times 14}{14\times 45\sqrt{7}}$$

Cancel out 3\times 14 in both numerator and denominator.

$$\frac{\sqrt{17}}{15\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{17}}{15\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{17}\sqrt{7}}{15\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{17}\sqrt{7}}{15\times 7}$$

To multiply \sqrt{17} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{119}}{15\times 7}$$

Multiply 15 and 7 to get 105.

$$\frac{\sqrt{119}}{105}$$