Solve 33/7/3sqrt{170/7}

$$\frac{ \frac{ 33 }{ 7 } }{ \frac{ 3 \sqrt{ 170 } }{ 7 } }$$

Evaluate

$$\frac{11\sqrt{170}}{170}\approx 0.843661488$$

Solution Steps

Divide \frac{33}{7} by \frac{3\sqrt{170}}{7} by multiplying \frac{33}{7} by the reciprocal of \frac{3\sqrt{170}}{7}.

$$\frac{33\times 7}{7\times 3\sqrt{170}}$$

Cancel out 3\times 7 in both numerator and denominator.

$$\frac{11}{\sqrt{170}}$$

Rationalize the denominator of \frac{11}{\sqrt{170}} by multiplying numerator and denominator by \sqrt{170}.

$$\frac{11\sqrt{170}}{\left(\sqrt{170}\right)^{2}}$$

The square of \sqrt{170} is 170.

$$\frac{11\sqrt{170}}{170}$$