Solve 8826-47,25+34/9+0,766-sqrt{16}

$$8826 - 47,25 + 34 / 9 + 0,766 - \sqrt { 16 }$$

Evaluate

$$\frac{19753411}{2250}\approx 8779,293777778$$

Solution Steps

Subtract 47,25 from 8826 to get 8778,75.

$$8778,75+\frac{34}{9}+0,766-\sqrt{16}$$

Convert decimal number 8778,75 to fraction \frac{877875}{100}. Reduce the fraction \frac{877875}{100} to lowest terms by extracting and canceling out 25.

$$\frac{35115}{4}+\frac{34}{9}+0,766-\sqrt{16}$$

Least common multiple of 4 and 9 is 36. Convert \frac{35115}{4} and \frac{34}{9} to fractions with denominator 36.

$$\frac{316035}{36}+\frac{136}{36}+0,766-\sqrt{16}$$

Since \frac{316035}{36} and \frac{136}{36} have the same denominator, add them by adding their numerators.

$$\frac{316035+136}{36}+0,766-\sqrt{16}$$

Add 316035 and 136 to get 316171.

$$\frac{316171}{36}+0,766-\sqrt{16}$$

Convert decimal number 0,766 to fraction \frac{766}{1000}. Reduce the fraction \frac{766}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{316171}{36}+\frac{383}{500}-\sqrt{16}$$

Least common multiple of 36 and 500 is 4500. Convert \frac{316171}{36} and \frac{383}{500} to fractions with denominator 4500.

$$\frac{39521375}{4500}+\frac{3447}{4500}-\sqrt{16}$$

Since \frac{39521375}{4500} and \frac{3447}{4500} have the same denominator, add them by adding their numerators.

$$\frac{39521375+3447}{4500}-\sqrt{16}$$

Add 39521375 and 3447 to get 39524822.

$$\frac{39524822}{4500}-\sqrt{16}$$

Reduce the fraction \frac{39524822}{4500} to lowest terms by extracting and canceling out 2.

$$\frac{19762411}{2250}-\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$\frac{19762411}{2250}-4$$

Convert 4 to fraction \frac{9000}{2250}.

$$\frac{19762411}{2250}-\frac{9000}{2250}$$

Since \frac{19762411}{2250} and \frac{9000}{2250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19762411-9000}{2250}$$

Subtract 9000 from 19762411 to get 19753411.

$$\frac{19753411}{2250}$$

Factor

$$\frac{191 \cdot 103421}{2 \cdot 3 ^ {2} \cdot 5 ^ {3}} = 8779\frac{661}{2250} = 8779.293777777777$$