Solve sqrt{0.495^2/1-0.495^2}

$$\sqrt{ \frac{ { 0.495 }^{ 2 } }{ 1- { 0.495 }^{ 2 } } }$$

Evaluate

$$\frac{99\sqrt{30199}}{30199}\approx 0.569690416$$

Solution Steps

Calculate 0.495 to the power of 2 and get 0.245025.

$$\sqrt{\frac{0.245025}{1-0.495^{2}}}$$

Calculate 0.495 to the power of 2 and get 0.245025.

$$\sqrt{\frac{0.245025}{1-0.245025}}$$

Subtract 0.245025 from 1 to get 0.754975.

$$\sqrt{\frac{0.245025}{0.754975}}$$

Expand \frac{0.245025}{0.754975} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{245025}{754975}}$$

Reduce the fraction \frac{245025}{754975} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{9801}{30199}}$$

Rewrite the square root of the division \sqrt{\frac{9801}{30199}} as the division of square roots \frac{\sqrt{9801}}{\sqrt{30199}}.

$$\frac{\sqrt{9801}}{\sqrt{30199}}$$

Calculate the square root of 9801 and get 99.

$$\frac{99}{\sqrt{30199}}$$

Rationalize the denominator of \frac{99}{\sqrt{30199}} by multiplying numerator and denominator by \sqrt{30199}.

$$\frac{99\sqrt{30199}}{\left(\sqrt{30199}\right)^{2}}$$

The square of \sqrt{30199} is 30199.

$$\frac{99\sqrt{30199}}{30199}$$