Solve frac{2sqrt{63}}{sqrt{18}}

$$\frac { 2 \sqrt { 63 } } { \sqrt { 18 } }$$

Evaluate

$$\sqrt{14}\approx 3.741657387$$

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}.

$$\frac{2\times 3\sqrt{7}}{\sqrt{18}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{7}}{\sqrt{18}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{6\sqrt{7}}{3\sqrt{2}}$$

Cancel out 3 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

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

$$\frac{2\sqrt{14}}{2}$$

Cancel out 2 and 2.

$$\sqrt{14}$$