Solve sqrt{0.55(1-0.55)/16}

$$\sqrt{ \frac{ 0.55(1-0.55) }{ 16 } }$$

Evaluate

$$\frac{3\sqrt{11}}{80}\approx 0.12437343$$

Solution Steps

Subtract 0.55 from 1 to get 0.45.

$$\sqrt{\frac{0.55\times 0.45}{16}}$$

Multiply 0.55 and 0.45 to get 0.2475.

$$\sqrt{\frac{0.2475}{16}}$$

Expand \frac{0.2475}{16} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{2475}{160000}}$$

Reduce the fraction \frac{2475}{160000} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{99}{6400}}$$

Rewrite the square root of the division \sqrt{\frac{99}{6400}} as the division of square roots \frac{\sqrt{99}}{\sqrt{6400}}.

$$\frac{\sqrt{99}}{\sqrt{6400}}$$

Factor 99=3^{2}\times 11. Rewrite the square root of the product \sqrt{3^{2}\times 11} as the product of square roots \sqrt{3^{2}}\sqrt{11}. Take the square root of 3^{2}.

$$\frac{3\sqrt{11}}{\sqrt{6400}}$$

Calculate the square root of 6400 and get 80.

$$\frac{3\sqrt{11}}{80}$$