Solve 17*19*21/[(12.1)^2-(8.1)^2]div[(0.25)^2+(0.25)(19.95)]

$$\frac { 17 \times 19 \times 21 } { [ ( 12.1 ) ^ { 2 } - ( 8.1 ) ^ { 2 } ] \div [ ( 0.25 ) ^ { 2 } + ( 0.25 ) ( 19.95 ) ] }$$

Evaluate

$$423.9375$$

Solution Steps

Multiply 17 and 19 to get 323.

$$\frac{323\times 21}{\frac{12.1^{2}-8.1^{2}}{0.25^{2}+0.25\times 19.95}}$$

Multiply 323 and 21 to get 6783.

$$\frac{6783}{\frac{12.1^{2}-8.1^{2}}{0.25^{2}+0.25\times 19.95}}$$

Calculate 12.1 to the power of 2 and get 146.41.

$$\frac{6783}{\frac{146.41-8.1^{2}}{0.25^{2}+0.25\times 19.95}}$$

Calculate 8.1 to the power of 2 and get 65.61.

$$\frac{6783}{\frac{146.41-65.61}{0.25^{2}+0.25\times 19.95}}$$

Subtract 65.61 from 146.41 to get 80.8.

$$\frac{6783}{\frac{80.8}{0.25^{2}+0.25\times 19.95}}$$

Calculate 0.25 to the power of 2 and get 0.0625.

$$\frac{6783}{\frac{80.8}{0.0625+0.25\times 19.95}}$$

Multiply 0.25 and 19.95 to get 4.9875.

$$\frac{6783}{\frac{80.8}{0.0625+4.9875}}$$

Add 0.0625 and 4.9875 to get 5.05.

$$\frac{6783}{\frac{80.8}{5.05}}$$

Expand \frac{80.8}{5.05} by multiplying both numerator and the denominator by 100.

$$\frac{6783}{\frac{8080}{505}}$$

Divide 8080 by 505 to get 16.

$$\frac{6783}{16}$$

Factor

$$\frac{3 \cdot 7 \cdot 17 \cdot 19}{2 ^ {4}} = 423\frac{15}{16} = 423.9375$$