Evaluate (0.191-0.220)+1.645 square root of ((0.191)(0.809))/174+((0.220)(0.780))/141

$(0.191 - 0.22) + 1.645 \sqrt{\frac{(0.191) (0.809)}{174} + \frac{(0.22) (0.78)}{141}}$

Step 1

Simplify each term.

To write $\frac{(0.191) (0.809)}{174}$ as a fraction with a common denominator, multiply by $\frac{47}{47}$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{(0.191) (0.809)}{174} \cdot \frac{47}{47} + \frac{(0.22) (0.78)}{141}}$

To write $\frac{(0.22) (0.78)}{141}$ as a fraction with a common denominator, multiply by $\frac{58}{58}$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{(0.191) (0.809)}{174} \cdot \frac{47}{47} + \frac{(0.22) (0.78)}{141} \cdot \frac{58}{58}}$

Write each expression with a common denominator of $8178$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{(0.191) (0.809)}{174}$ by $\frac{47}{47}$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{(0.191) (0.809) \cdot 47}{174 \cdot 47} + \frac{(0.22) (0.78)}{141} \cdot \frac{58}{58}}$

Multiply $174$ by $47$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{(0.191) (0.809) \cdot 47}{8178} + \frac{(0.22) (0.78)}{141} \cdot \frac{58}{58}}$

Multiply $\frac{(0.22) (0.78)}{141}$ by $\frac{58}{58}$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{(0.191) (0.809) \cdot 47}{8178} + \frac{(0.22) (0.78) \cdot 58}{141 \cdot 58}}$

Multiply $141$ by $58$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{(0.191) (0.809) \cdot 47}{8178} + \frac{(0.22) (0.78) \cdot 58}{8178}}$

Combine the numerators over the common denominator.

$0.191 - 0.22 + 1.645 \sqrt{\frac{(0.191) (0.809) \cdot 47 + (0.22) (0.78) \cdot 58}{8178}}$

Rewrite $\frac{(0.191) (0.809) \cdot 47 + (0.22) (0.78) \cdot 58}{8178}$ in a factored form.

Multiply $(0.191) (0.809) \cdot 47$ .

Multiply $0.191$ by $0.809$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{0.154519 \cdot 47 + (0.22) (0.78) \cdot 58}{8178}}$

Multiply $0.154519$ by $47$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{7.262393 + (0.22) (0.78) \cdot 58}{8178}}$

Multiply $(0.22) (0.78) \cdot 58$ .

Multiply $0.22$ by $0.78$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{7.262393 + 0.1716 \cdot 58}{8178}}$

Multiply $0.1716$ by $58$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{7.262393 + 9.9528}{8178}}$

Add $7.262393$ and $9.9528$ .

$0.191 - 0.22 + 1.645 \sqrt{\frac{17.215193}{8178}}$

Divide $17.215193$ by $8178$ .

$0.191 - 0.22 + 1.645 \sqrt{0.00210506}$

Multiply $1.645$ by $\sqrt{0.00210506}$ .

$0.191 - 0.22 + 0.07547416$

Step 2

Simplify by adding and subtracting.

Subtract $0.22$ from $0.191$ .

$- 0.029 + 0.07547416$

Add $- 0.029$ and $0.07547416$ .

$0.04647416$