Solve 6sqrt{7/18}

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

Evaluate

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

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{18}} as the division of square roots \frac{\sqrt{7}}{\sqrt{18}}.

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

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}.

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

Rationalize the denominator of \frac{\sqrt{7}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$6\times \frac{\sqrt{7}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

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

$$6\times \frac{\sqrt{14}}{3\times 2}$$

Multiply 3 and 2 to get 6.

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

Cancel out 6 and 6.

$$\sqrt{14}$$