Solve sqrt{3/14}divsqrt{42/3}

$$\sqrt { \frac { 3 } { 14 } } \div \sqrt { 4 \frac { 2 } { 3 } }$$

Evaluate

$$\frac{3}{14}\approx 0.214285714$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{14}} as the division of square roots \frac{\sqrt{3}}{\sqrt{14}}.

$$\frac{\frac{\sqrt{3}}{\sqrt{14}}}{\sqrt{\frac{4\times 3+2}{3}}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\frac{\sqrt{3}\sqrt{14}}{\left(\sqrt{14}\right)^{2}}}{\sqrt{\frac{4\times 3+2}{3}}}$$

The square of \sqrt{14} is 14.

$$\frac{\frac{\sqrt{3}\sqrt{14}}{14}}{\sqrt{\frac{4\times 3+2}{3}}}$$

To multiply \sqrt{3} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{42}}{14}}{\sqrt{\frac{4\times 3+2}{3}}}$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{\sqrt{42}}{14}}{\sqrt{\frac{12+2}{3}}}$$

Add 12 and 2 to get 14.

$$\frac{\frac{\sqrt{42}}{14}}{\sqrt{\frac{14}{3}}}$$

Rewrite the square root of the division \sqrt{\frac{14}{3}} as the division of square roots \frac{\sqrt{14}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{42}}{14}}{\frac{\sqrt{14}}{\sqrt{3}}}$$

Rationalize the denominator of \frac{\sqrt{14}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{\sqrt{42}}{14}}{\frac{\sqrt{14}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{\sqrt{42}}{14}}{\frac{\sqrt{14}\sqrt{3}}{3}}$$

To multiply \sqrt{14} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{42}}{14}}{\frac{\sqrt{42}}{3}}$$

Divide \frac{\sqrt{42}}{14} by \frac{\sqrt{42}}{3} by multiplying \frac{\sqrt{42}}{14} by the reciprocal of \frac{\sqrt{42}}{3}.

$$\frac{\sqrt{42}\times 3}{14\sqrt{42}}$$

Cancel out \sqrt{42} in both numerator and denominator.

$$\frac{3}{14}$$

Factor

$$\frac{3}{2 \cdot 7} = 0.21428571428571427$$