Solve sqrt{0.14^2/1-0.14^2}

$$\sqrt{ \frac{ { 0.14 }^{ 2 } }{ 1- { 0.14 }^{ 2 } } }$$

Evaluate

$$\frac{7\sqrt{2451}}{2451}\approx 0.141392504$$

Solution Steps

Calculate 0.14 to the power of 2 and get 0.0196.

$$\sqrt{\frac{0.0196}{1-0.14^{2}}}$$

Calculate 0.14 to the power of 2 and get 0.0196.

$$\sqrt{\frac{0.0196}{1-0.0196}}$$

Subtract 0.0196 from 1 to get 0.9804.

$$\sqrt{\frac{0.0196}{0.9804}}$$

Expand \frac{0.0196}{0.9804} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{196}{9804}}$$

Reduce the fraction \frac{196}{9804} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{49}{2451}}$$

Rewrite the square root of the division \sqrt{\frac{49}{2451}} as the division of square roots \frac{\sqrt{49}}{\sqrt{2451}}.

$$\frac{\sqrt{49}}{\sqrt{2451}}$$

Calculate the square root of 49 and get 7.

$$\frac{7}{\sqrt{2451}}$$

Rationalize the denominator of \frac{7}{\sqrt{2451}} by multiplying numerator and denominator by \sqrt{2451}.

$$\frac{7\sqrt{2451}}{\left(\sqrt{2451}\right)^{2}}$$

The square of \sqrt{2451} is 2451.

$$\frac{7\sqrt{2451}}{2451}$$