Solve sqrt{.25(1-.25)/60}

$$\sqrt{ \frac{ .25(1-.25) }{ 60 } }$$

Evaluate

$$\frac{\sqrt{5}}{40}\approx 0.055901699$$

Solution Steps

Subtract 0.25 from 1 to get 0.75.

$$\sqrt{\frac{0.25\times 0.75}{60}}$$

Multiply 0.25 and 0.75 to get 0.1875.

$$\sqrt{\frac{0.1875}{60}}$$

Expand \frac{0.1875}{60} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{1875}{600000}}$$

Reduce the fraction \frac{1875}{600000} to lowest terms by extracting and canceling out 1875.

$$\sqrt{\frac{1}{320}}$$

Rewrite the square root of the division \sqrt{\frac{1}{320}} as the division of square roots \frac{\sqrt{1}}{\sqrt{320}}.

$$\frac{\sqrt{1}}{\sqrt{320}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{320}}$$

Factor 320=8^{2}\times 5. Rewrite the square root of the product \sqrt{8^{2}\times 5} as the product of square roots \sqrt{8^{2}}\sqrt{5}. Take the square root of 8^{2}.

$$\frac{1}{8\sqrt{5}}$$

Rationalize the denominator of \frac{1}{8\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{8\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{8\times 5}$$

Multiply 8 and 5 to get 40.

$$\frac{\sqrt{5}}{40}$$