Solve 79852.5*(3-1/3*(0.12^2+2*0.06^2+0.373^2)

$$79852.5 \times (3- \frac { 1 } { 3 } \times ( { 0.12 }^{ 2 } +2 \times { 0.06 }^{ 2 } + { 0.373 }^{ 2 } )$$

Evaluate

$$235279.2958425$$

Solution Steps

Calculate 0.12 to the power of 2 and get 0.0144.

$$79852.5\left(3-\frac{1}{3}\left(0.0144+2\times 0.06^{2}+0.373^{2}\right)\right)$$

Calculate 0.06 to the power of 2 and get 0.0036.

$$79852.5\left(3-\frac{1}{3}\left(0.0144+2\times 0.0036+0.373^{2}\right)\right)$$

Multiply 2 and 0.0036 to get 0.0072.

$$79852.5\left(3-\frac{1}{3}\left(0.0144+0.0072+0.373^{2}\right)\right)$$

Add 0.0144 and 0.0072 to get 0.0216.

$$79852.5\left(3-\frac{1}{3}\left(0.0216+0.373^{2}\right)\right)$$

Calculate 0.373 to the power of 2 and get 0.139129.

$$79852.5\left(3-\frac{1}{3}\left(0.0216+0.139129\right)\right)$$

Add 0.0216 and 0.139129 to get 0.160729.

$$79852.5\left(3-\frac{1}{3}\times 0.160729\right)$$

Convert decimal number 0.160729 to fraction \frac{160729}{1000000}.

$$79852.5\left(3-\frac{1}{3}\times \frac{160729}{1000000}\right)$$

Multiply \frac{1}{3} times \frac{160729}{1000000} by multiplying numerator times numerator and denominator times denominator.

$$79852.5\left(3-\frac{1\times 160729}{3\times 1000000}\right)$$

Do the multiplications in the fraction \frac{1\times 160729}{3\times 1000000}.

$$79852.5\left(3-\frac{160729}{3000000}\right)$$

Convert 3 to fraction \frac{9000000}{3000000}.

$$79852.5\left(\frac{9000000}{3000000}-\frac{160729}{3000000}\right)$$

Since \frac{9000000}{3000000} and \frac{160729}{3000000} have the same denominator, subtract them by subtracting their numerators.

$$79852.5\times \frac{9000000-160729}{3000000}$$

Subtract 160729 from 9000000 to get 8839271.

$$79852.5\times \frac{8839271}{3000000}$$

Convert decimal number 79852.5 to fraction \frac{798525}{10}. Reduce the fraction \frac{798525}{10} to lowest terms by extracting and canceling out 5.

$$\frac{159705}{2}\times \frac{8839271}{3000000}$$

Multiply \frac{159705}{2} times \frac{8839271}{3000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{159705\times 8839271}{2\times 3000000}$$

Do the multiplications in the fraction \frac{159705\times 8839271}{2\times 3000000}.

$$\frac{1411675775055}{6000000}$$

Reduce the fraction \frac{1411675775055}{6000000} to lowest terms by extracting and canceling out 15.

$$\frac{94111718337}{400000}$$

Factor

$$\frac{1262753 \cdot 3 ^ {2} \cdot 7 ^ {2} \cdot 13 ^ {2}}{2 ^ {7} \cdot 5 ^ {5}} = 235279\frac{118337}{400000} = 235279.2958425$$