Solve sqrt{(22div12.7)}

$$\sqrt{ (22 \div 12.7) }$$

Evaluate

$$\frac{2\sqrt{6985}}{127}\approx 1.316162401$$

Solution Steps

Expand \frac{22}{12.7} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{220}{127}}$$

Rewrite the square root of the division \sqrt{\frac{220}{127}} as the division of square roots \frac{\sqrt{220}}{\sqrt{127}}.

$$\frac{\sqrt{220}}{\sqrt{127}}$$

Factor 220=2^{2}\times 55. Rewrite the square root of the product \sqrt{2^{2}\times 55} as the product of square roots \sqrt{2^{2}}\sqrt{55}. Take the square root of 2^{2}.

$$\frac{2\sqrt{55}}{\sqrt{127}}$$

Rationalize the denominator of \frac{2\sqrt{55}}{\sqrt{127}} by multiplying numerator and denominator by \sqrt{127}.

$$\frac{2\sqrt{55}\sqrt{127}}{\left(\sqrt{127}\right)^{2}}$$

The square of \sqrt{127} is 127.

$$\frac{2\sqrt{55}\sqrt{127}}{127}$$

To multiply \sqrt{55} and \sqrt{127}, multiply the numbers under the square root.

$$\frac{2\sqrt{6985}}{127}$$