Solve 3/8{{left(1+1frac{1/2right)}^2}}

$$\frac{ 3 }{ \frac{ 8 }{ { \left(1+1 \frac{ 1 }{ 2 } \right) }^{ 2 } } }$$

Evaluate

$$\frac{75}{32}=2.34375$$

Solution Steps

Divide 3 by \frac{8}{\left(1+\frac{1\times 2+1}{2}\right)^{2}} by multiplying 3 by the reciprocal of \frac{8}{\left(1+\frac{1\times 2+1}{2}\right)^{2}}.

$$\frac{3\left(1+\frac{1\times 2+1}{2}\right)^{2}}{8}$$

Multiply 1 and 2 to get 2.

$$\frac{3\left(1+\frac{2+1}{2}\right)^{2}}{8}$$

Add 2 and 1 to get 3.

$$\frac{3\left(1+\frac{3}{2}\right)^{2}}{8}$$

Add 1 and \frac{3}{2} to get \frac{5}{2}.

$$\frac{3\times \left(\frac{5}{2}\right)^{2}}{8}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{3\times \frac{25}{4}}{8}$$

Multiply 3 and \frac{25}{4} to get \frac{75}{4}.

$$\frac{\frac{75}{4}}{8}$$

Express \frac{\frac{75}{4}}{8} as a single fraction.

$$\frac{75}{4\times 8}$$

Multiply 4 and 8 to get 32.

$$\frac{75}{32}$$

Factor

$$\frac{3 \cdot 5 ^ {2}}{2 ^ {5}} = 2\frac{11}{32} = 2.34375$$