Solve frac{3sqrt{2}}{sqrt{63}}

$$\frac { 3 \sqrt { 2 } } { \sqrt { 63 } }$$

Evaluate

$$\frac{\sqrt{14}}{7}\approx 0.534522484$$

Solution Steps

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

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

Cancel out 3 in both numerator and denominator.

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

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

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

The square of \sqrt{7} is 7.

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

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

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