Solve 0.0733-0.05/sqrt{frac{0.05*0.95{475}}}

$$\frac{ 0.0733-0.05 }{ \sqrt{ \frac{ 0.05 \cdot 0.95 }{ 475 } } }$$

Evaluate

$$\frac{233\sqrt{10000}}{10000}\approx 2.33$$

Solution Steps

Subtract 0.05 from 0.0733 to get 0.0233.

$$\frac{0.0233}{\sqrt{\frac{0.05\times 0.95}{475}}}$$

Multiply 0.05 and 0.95 to get 0.0475.

$$\frac{0.0233}{\sqrt{\frac{0.0475}{475}}}$$

Expand \frac{0.0475}{475} by multiplying both numerator and the denominator by 10000.

$$\frac{0.0233}{\sqrt{\frac{475}{4750000}}}$$

Reduce the fraction \frac{475}{4750000} to lowest terms by extracting and canceling out 475.

$$\frac{0.0233}{\sqrt{\frac{1}{10000}}}$$

Rewrite the square root of the division \frac{1}{10000} as the division of square roots \frac{\sqrt{1}}{\sqrt{10000}}. Take the square root of both numerator and denominator.

$$\frac{0.0233}{\frac{1}{100}}$$

Divide 0.0233 by \frac{1}{100} by multiplying 0.0233 by the reciprocal of \frac{1}{100}.

$$0.0233\times 100$$

Multiply 0.0233 and 100 to get 2.33.

$$2.33$$