Solve {left(3/21/4+1/510/3right)}^2+1=

$${ \left( \frac{ 3 }{ 2 } \frac{ 1 }{ 4 } + \frac{ 1 }{ 5 } \frac{ 10 }{ 3 } \right) }^{ 2 } +1=$$

Evaluate

$$\frac{1201}{576}\approx 2.085069444$$

Solution Steps

Multiply \frac{3}{2} and \frac{1}{4} to get \frac{3}{8}.

$$\left(\frac{3}{8}+\frac{1}{5}\times \frac{10}{3}\right)^{2}+1$$

Multiply \frac{1}{5} and \frac{10}{3} to get \frac{2}{3}.

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

Add \frac{3}{8} and \frac{2}{3} to get \frac{25}{24}.

$$\left(\frac{25}{24}\right)^{2}+1$$

Calculate \frac{25}{24} to the power of 2 and get \frac{625}{576}.

$$\frac{625}{576}+1$$

Add \frac{625}{576} and 1 to get \frac{1201}{576}.

$$\frac{1201}{576}$$

Factor

$$\frac{1201}{2 ^ {6} \cdot 3 ^ {2}} = 2\frac{49}{576} = 2.0850694444444446$$