Solve {left(9/8right)}^2+2*9/8*1/12+{left(1/12right)}^2

$${ \left( \frac{ 9 }{ 8 } \right) }^{ 2 } +2 \times \frac{ 9 }{ 8 } \times \frac{ 1 }{ 12 } + { \left( \frac{ 1 }{ 12 } \right) }^{ 2 }$$

Evaluate

$$\frac{841}{576}\approx 1.460069444$$

Solution Steps

Calculate \frac{9}{8} to the power of 2 and get \frac{81}{64}.

$$\frac{81}{64}+2\times \frac{9}{8}\times \frac{1}{12}+\left(\frac{1}{12}\right)^{2}$$

Express 2\times \frac{9}{8} as a single fraction.

$$\frac{81}{64}+\frac{2\times 9}{8}\times \frac{1}{12}+\left(\frac{1}{12}\right)^{2}$$

Multiply 2 and 9 to get 18.

$$\frac{81}{64}+\frac{18}{8}\times \frac{1}{12}+\left(\frac{1}{12}\right)^{2}$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

$$\frac{81}{64}+\frac{9}{4}\times \frac{1}{12}+\left(\frac{1}{12}\right)^{2}$$

Multiply \frac{9}{4} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81}{64}+\frac{9\times 1}{4\times 12}+\left(\frac{1}{12}\right)^{2}$$

Do the multiplications in the fraction \frac{9\times 1}{4\times 12}.

$$\frac{81}{64}+\frac{9}{48}+\left(\frac{1}{12}\right)^{2}$$

Reduce the fraction \frac{9}{48} to lowest terms by extracting and canceling out 3.

$$\frac{81}{64}+\frac{3}{16}+\left(\frac{1}{12}\right)^{2}$$

Least common multiple of 64 and 16 is 64. Convert \frac{81}{64} and \frac{3}{16} to fractions with denominator 64.

$$\frac{81}{64}+\frac{12}{64}+\left(\frac{1}{12}\right)^{2}$$

Since \frac{81}{64} and \frac{12}{64} have the same denominator, add them by adding their numerators.

$$\frac{81+12}{64}+\left(\frac{1}{12}\right)^{2}$$

Add 81 and 12 to get 93.

$$\frac{93}{64}+\left(\frac{1}{12}\right)^{2}$$

Calculate \frac{1}{12} to the power of 2 and get \frac{1}{144}.

$$\frac{93}{64}+\frac{1}{144}$$

Least common multiple of 64 and 144 is 576. Convert \frac{93}{64} and \frac{1}{144} to fractions with denominator 576.

$$\frac{837}{576}+\frac{4}{576}$$

Since \frac{837}{576} and \frac{4}{576} have the same denominator, add them by adding their numerators.

$$\frac{837+4}{576}$$

Add 837 and 4 to get 841.

$$\frac{841}{576}$$

Factor

$$\frac{29 ^ {2}}{2 ^ {6} \cdot 3 ^ {2}} = 1\frac{265}{576} = 1.4600694444444444$$