Solve sqrt{232.8/6}

$$\sqrt{ \frac{ 232.8 }{ 6 } }$$

Evaluate

$$\frac{\sqrt{970}}{5}\approx 6.228964601$$

Solution Steps

Expand \frac{232.8}{6} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{2328}{60}}$$

Reduce the fraction \frac{2328}{60} to lowest terms by extracting and canceling out 12.

$$\sqrt{\frac{194}{5}}$$

Rewrite the square root of the division \sqrt{\frac{194}{5}} as the division of square roots \frac{\sqrt{194}}{\sqrt{5}}.

$$\frac{\sqrt{194}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{194}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{194}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{194}\sqrt{5}}{5}$$

To multiply \sqrt{194} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{970}}{5}$$