Answer
The friend is incorrect.
$\left(4\frac{1}{3}\right)^{2}$ is equal to $16\frac{25}{9}$ when evaluated using the square of a binomial pattern.
Work Step by Step
Using the square of a binomial pattern, we have
$\left(4\frac{1}{3}\right)^{2}=\left(4+\frac{1}{3}\right)^{2}=4^{2}+2(4)\left(\frac{1}{3}\right)+\left(\frac{1}{3}\right)^{2}$
$=16+\frac{8}{3}+\frac{1}{9}=16+\frac{25}{9}=16\frac{25}{9}$.
The friend is incorrect. He squared the integer part and the fraction part and placed the two results near each other.
