Solve sqrt{2237.2/4}

$$\sqrt{ \frac{ 2237.2 }{ 4 } }$$

Evaluate

$$\frac{\sqrt{55930}}{10}\approx 23.649524308$$

Solution Steps

Expand \frac{2237.2}{4} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{22372}{40}}$$

Reduce the fraction \frac{22372}{40} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{5593}{10}}$$

Rewrite the square root of the division \sqrt{\frac{5593}{10}} as the division of square roots \frac{\sqrt{5593}}{\sqrt{10}}.

$$\frac{\sqrt{5593}}{\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{5593}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{5593}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{5593}\sqrt{10}}{10}$$

To multiply \sqrt{5593} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{55930}}{10}$$