Solve frac{sqrt{14}}{3}divfrac{sqrt{162}}{6}

$$\frac { \sqrt { 14 } } { 3 } \div \frac { \sqrt { 162 } } { 6 }$$

Evaluate

$$\frac{2\sqrt{7}}{9}\approx 0.587944736$$

Solution Steps

Divide \frac{\sqrt{14}}{3} by \frac{\sqrt{162}}{6} by multiplying \frac{\sqrt{14}}{3} by the reciprocal of \frac{\sqrt{162}}{6}.

$$\frac{\sqrt{14}\times 6}{3\sqrt{162}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\sqrt{14}}{\sqrt{162}}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$\frac{2\sqrt{14}}{9\sqrt{2}}$$

Rationalize the denominator of \frac{2\sqrt{14}}{9\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{2\sqrt{14}\sqrt{2}}{9\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{2\sqrt{14}\sqrt{2}}{9\times 2}$$

Factor 14=2\times 7. Rewrite the square root of the product \sqrt{2\times 7} as the product of square roots \sqrt{2}\sqrt{7}.

$$\frac{2\sqrt{2}\sqrt{7}\sqrt{2}}{9\times 2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2\times 2\sqrt{7}}{9\times 2}$$

Multiply 9 and 2 to get 18.

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

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{7}}{18}$$

Divide 4\sqrt{7} by 18 to get \frac{2}{9}\sqrt{7}.

$$\frac{2}{9}\sqrt{7}$$