Solve 0.5+1.96sqrt{0.5*0.5/100}

$$0.5+1.96 \sqrt{ \frac{ 0.5 \cdot 0.5 }{ 100 } }$$

Evaluate

$$0.598$$

Solution Steps

Multiply 0.5 and 0.5 to get 0.25.

$$0.5+1.96\sqrt{\frac{0.25}{100}}$$

Expand \frac{0.25}{100} by multiplying both numerator and the denominator by 100.

$$0.5+1.96\sqrt{\frac{25}{10000}}$$

Reduce the fraction \frac{25}{10000} to lowest terms by extracting and canceling out 25.

$$0.5+1.96\sqrt{\frac{1}{400}}$$

Rewrite the square root of the division \frac{1}{400} as the division of square roots \frac{\sqrt{1}}{\sqrt{400}}. Take the square root of both numerator and denominator.

$$0.5+1.96\times \frac{1}{20}$$

Convert decimal number 1.96 to fraction \frac{196}{100}. Reduce the fraction \frac{196}{100} to lowest terms by extracting and canceling out 4.

$$0.5+\frac{49}{25}\times \frac{1}{20}$$

Multiply \frac{49}{25} times \frac{1}{20} by multiplying numerator times numerator and denominator times denominator.

$$0.5+\frac{49\times 1}{25\times 20}$$

Do the multiplications in the fraction \frac{49\times 1}{25\times 20}.

$$0.5+\frac{49}{500}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}+\frac{49}{500}$$

Least common multiple of 2 and 500 is 500. Convert \frac{1}{2} and \frac{49}{500} to fractions with denominator 500.

$$\frac{250}{500}+\frac{49}{500}$$

Since \frac{250}{500} and \frac{49}{500} have the same denominator, add them by adding their numerators.

$$\frac{250+49}{500}$$

Add 250 and 49 to get 299.

$$\frac{299}{500}$$

Factor

$$\frac{13 \cdot 23}{2 ^ {2} \cdot 5 ^ {3}} = 0.598$$