### Instruction: Evaluate $\left|\frac56 +2i\right|$.### Response: I recognize that this is a complex number in the form $a+bi$, where $a=\frac56$ and $b=2$.
I also know that the absolute value of a complex number is the same as its distance from the origin in the complex plane, which can be found using the Pythagorean theorem.
So, I need to find the length of the hypotenuse of a right triangle with legs of length $\frac56$ and $2$.
To do that, I square both legs and add them, then take the square root of the result: $\left|\frac56 +2i\right|=\sqrt{\left(\frac56\right)^2+(2)^2}$.
I simplify the expression inside the square root: $\left|\frac56 +2i\right|=\sqrt{\frac{25}{36}+4}$.
I convert the fraction to a decimal and combine the terms: $\left|\frac56 +2i\right|=\sqrt{0.6944+4}$.