Solve 7div2-[21div4div((2+5)*(25div8)div(5div2))^2]

$$7 \div 2 - [ 21 \div 4 \div ( ( 2 + 5 ) \times ( 25 \div 8 ) \div ( 5 \div 2 ) ) ^ { 2 } ]$$

Evaluate

$$\frac{1201}{350}\approx 3.431428571$$

Solution Steps

Add 2 and 5 to get 7.

$$\frac{7}{2}-\frac{\frac{21}{4}}{\left(\frac{7\times \frac{25}{8}}{\frac{5}{2}}\right)^{2}}$$

Multiply 7 and \frac{25}{8} to get \frac{175}{8}.

$$\frac{7}{2}-\frac{\frac{21}{4}}{\left(\frac{\frac{175}{8}}{\frac{5}{2}}\right)^{2}}$$

Divide \frac{175}{8} by \frac{5}{2} by multiplying \frac{175}{8} by the reciprocal of \frac{5}{2}.

$$\frac{7}{2}-\frac{\frac{21}{4}}{\left(\frac{175}{8}\times \frac{2}{5}\right)^{2}}$$

Multiply \frac{175}{8} and \frac{2}{5} to get \frac{35}{4}.

$$\frac{7}{2}-\frac{\frac{21}{4}}{\left(\frac{35}{4}\right)^{2}}$$

Calculate \frac{35}{4} to the power of 2 and get \frac{1225}{16}.

$$\frac{7}{2}-\frac{\frac{21}{4}}{\frac{1225}{16}}$$

Divide \frac{21}{4} by \frac{1225}{16} by multiplying \frac{21}{4} by the reciprocal of \frac{1225}{16}.

$$\frac{7}{2}-\frac{21}{4}\times \frac{16}{1225}$$

Multiply \frac{21}{4} and \frac{16}{1225} to get \frac{12}{175}.

$$\frac{7}{2}-\frac{12}{175}$$

Subtract \frac{12}{175} from \frac{7}{2} to get \frac{1201}{350}.

$$\frac{1201}{350}$$

Factor

$$\frac{1201}{2 \cdot 5 ^ {2} \cdot 7} = 3\frac{151}{350} = 3.4314285714285715$$