Solve sqrt{33/14/frac{154{21}}}

$$\sqrt { \frac { \frac { 33 } { 14 } } { \frac { 154 } { 21 } } }$$

Evaluate

$$\frac{3\sqrt{7}}{14}\approx 0.56694671$$

Solution Steps

Divide \frac{33}{14} by \frac{154}{21} by multiplying \frac{33}{14} by the reciprocal of \frac{154}{21}.

$$\sqrt{\frac{33\times 21}{14\times 154}}$$

Cancel out 7\times 11 in both numerator and denominator.

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

Multiply 3 and 3 to get 9.

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

Multiply 2 and 14 to get 28.

$$\sqrt{\frac{9}{28}}$$

Rewrite the square root of the division \sqrt{\frac{9}{28}} as the division of square roots \frac{\sqrt{9}}{\sqrt{28}}.

$$\frac{\sqrt{9}}{\sqrt{28}}$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{28}}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{7} is 7.

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

Multiply 2 and 7 to get 14.

$$\frac{3\sqrt{7}}{14}$$