Solve 14+28{left(3/4right)}^2+{left(1/4right)}^2

$$14+28 { \left( \frac{ 3 }{ 4 } \right) }^{ 2 } + { \left( \frac{ 1 }{ 4 } \right) }^{ 2 }$$

Evaluate

$$\frac{477}{16}=29.8125$$

Solution Steps

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$14+28\times \frac{9}{16}+\left(\frac{1}{4}\right)^{2}$$

Express 28\times \frac{9}{16} as a single fraction.

$$14+\frac{28\times 9}{16}+\left(\frac{1}{4}\right)^{2}$$

Multiply 28 and 9 to get 252.

$$14+\frac{252}{16}+\left(\frac{1}{4}\right)^{2}$$

Reduce the fraction \frac{252}{16} to lowest terms by extracting and canceling out 4.

$$14+\frac{63}{4}+\left(\frac{1}{4}\right)^{2}$$

Convert 14 to fraction \frac{56}{4}.

$$\frac{56}{4}+\frac{63}{4}+\left(\frac{1}{4}\right)^{2}$$

Since \frac{56}{4} and \frac{63}{4} have the same denominator, add them by adding their numerators.

$$\frac{56+63}{4}+\left(\frac{1}{4}\right)^{2}$$

Add 56 and 63 to get 119.

$$\frac{119}{4}+\left(\frac{1}{4}\right)^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{119}{4}+\frac{1}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{119}{4} and \frac{1}{16} to fractions with denominator 16.

$$\frac{476}{16}+\frac{1}{16}$$

Since \frac{476}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{476+1}{16}$$

Add 476 and 1 to get 477.

$$\frac{477}{16}$$

Factor

$$\frac{3 ^ {2} \cdot 53}{2 ^ {4}} = 29\frac{13}{16} = 29.8125$$