Solve (400/36*9.8)^2*9.8/4

$$( \frac { 400 } { 36 \times 9.8 } ) ^ { 2 } \times \frac { 9.8 } { 4 }$$

Evaluate

$$\frac{12500}{3969}\approx 3.149407911$$

Solution Steps

Multiply 36 and 9.8 to get 352.8.

$$\left(\frac{400}{352.8}\right)^{2}\times \frac{9.8}{4}$$

Expand \frac{400}{352.8} by multiplying both numerator and the denominator by 10.

$$\left(\frac{4000}{3528}\right)^{2}\times \frac{9.8}{4}$$

Reduce the fraction \frac{4000}{3528} to lowest terms by extracting and canceling out 8.

$$\left(\frac{500}{441}\right)^{2}\times \frac{9.8}{4}$$

Calculate \frac{500}{441} to the power of 2 and get \frac{250000}{194481}.

$$\frac{250000}{194481}\times \frac{9.8}{4}$$

Expand \frac{9.8}{4} by multiplying both numerator and the denominator by 10.

$$\frac{250000}{194481}\times \frac{98}{40}$$

Reduce the fraction \frac{98}{40} to lowest terms by extracting and canceling out 2.

$$\frac{250000}{194481}\times \frac{49}{20}$$

Multiply \frac{250000}{194481} and \frac{49}{20} to get \frac{12500}{3969}.

$$\frac{12500}{3969}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {5}}{3 ^ {4} \cdot 7 ^ {2}} = 3\frac{593}{3969} = 3.1494079113126734$$