Solve sqrt{0.55(1-0.55)/14}

$$\sqrt{ \frac{ 0.55(1-0.55) }{ 14 } }$$

Evaluate

$$\frac{3\sqrt{154}}{280}\approx 0.132960789$$

Solution Steps

Subtract 0.55 from 1 to get 0.45.

$$\sqrt{\frac{0.55\times 0.45}{14}}$$

Multiply 0.55 and 0.45 to get 0.2475.

$$\sqrt{\frac{0.2475}{14}}$$

Expand \frac{0.2475}{14} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{2475}{140000}}$$

Reduce the fraction \frac{2475}{140000} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{99}{5600}}$$

Rewrite the square root of the division \sqrt{\frac{99}{5600}} as the division of square roots \frac{\sqrt{99}}{\sqrt{5600}}.

$$\frac{\sqrt{99}}{\sqrt{5600}}$$

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}.

$$\frac{3\sqrt{11}}{\sqrt{5600}}$$

Factor 5600=20^{2}\times 14. Rewrite the square root of the product \sqrt{20^{2}\times 14} as the product of square roots \sqrt{20^{2}}\sqrt{14}. Take the square root of 20^{2}.

$$\frac{3\sqrt{11}}{20\sqrt{14}}$$

Rationalize the denominator of \frac{3\sqrt{11}}{20\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{3\sqrt{11}\sqrt{14}}{20\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{3\sqrt{11}\sqrt{14}}{20\times 14}$$

To multiply \sqrt{11} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{3\sqrt{154}}{20\times 14}$$

Multiply 20 and 14 to get 280.

$$\frac{3\sqrt{154}}{280}$$