Solve sqrt{723div4.2}

$$\sqrt{ 723 \div 4.2 }$$

Evaluate

$$\frac{\sqrt{8435}}{7}\approx 13.120322296$$

Solution Steps

Expand \frac{723}{4.2} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{7230}{42}}$$

Reduce the fraction \frac{7230}{42} to lowest terms by extracting and canceling out 6.

$$\sqrt{\frac{1205}{7}}$$

Rewrite the square root of the division \sqrt{\frac{1205}{7}} as the division of square roots \frac{\sqrt{1205}}{\sqrt{7}}.

$$\frac{\sqrt{1205}}{\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{1205}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{1205}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{1205}\sqrt{7}}{7}$$

To multiply \sqrt{1205} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{8435}}{7}$$