Solve =(0.26^2/0.26+0.18+0.39^2/0.39+0.05)*30^2/4

$$= ( \frac { 0.26 ^ { 2 } } { 0.26 + 0.18 } + \frac { 0.39 ^ { 2 } } { 0.39 + 0.05 } ) * \frac { 30 ^ { 2 } } { 4 }$$

Evaluate

$$\frac{19773}{176}\approx 112.346590909$$

Solution Steps

Calculate 0.26 to the power of 2 and get 0.0676.

$$\left(\frac{0.0676}{0.26+0.18}+\frac{0.39^{2}}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Add 0.26 and 0.18 to get 0.44.

$$\left(\frac{0.0676}{0.44}+\frac{0.39^{2}}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Expand \frac{0.0676}{0.44} by multiplying both numerator and the denominator by 10000.

$$\left(\frac{676}{4400}+\frac{0.39^{2}}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Reduce the fraction \frac{676}{4400} to lowest terms by extracting and canceling out 4.

$$\left(\frac{169}{1100}+\frac{0.39^{2}}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Calculate 0.39 to the power of 2 and get 0.1521.

$$\left(\frac{169}{1100}+\frac{0.1521}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Add 0.39 and 0.05 to get 0.44.

$$\left(\frac{169}{1100}+\frac{0.1521}{0.44}\right)\times \frac{30^{2}}{4}$$

Expand \frac{0.1521}{0.44} by multiplying both numerator and the denominator by 10000.

$$\left(\frac{169}{1100}+\frac{1521}{4400}\right)\times \frac{30^{2}}{4}$$

Least common multiple of 1100 and 4400 is 4400. Convert \frac{169}{1100} and \frac{1521}{4400} to fractions with denominator 4400.

$$\left(\frac{676}{4400}+\frac{1521}{4400}\right)\times \frac{30^{2}}{4}$$

Since \frac{676}{4400} and \frac{1521}{4400} have the same denominator, add them by adding their numerators.

$$\frac{676+1521}{4400}\times \frac{30^{2}}{4}$$

Add 676 and 1521 to get 2197.

$$\frac{2197}{4400}\times \frac{30^{2}}{4}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{2197}{4400}\times \frac{900}{4}$$

Divide 900 by 4 to get 225.

$$\frac{2197}{4400}\times 225$$

Express \frac{2197}{4400}\times 225 as a single fraction.

$$\frac{2197\times 225}{4400}$$

Multiply 2197 and 225 to get 494325.

$$\frac{494325}{4400}$$

Reduce the fraction \frac{494325}{4400} to lowest terms by extracting and canceling out 25.

$$\frac{19773}{176}$$

Factor

$$\frac{3 ^ {2} \cdot 13 ^ {3}}{11 \cdot 2 ^ {4}} = 112\frac{61}{176} = 112.3465909090909$$