If ${\mathrm{a}}^{\mathrm{b}}={\mathrm{b}}^{\mathrm{a}}; (\mathrm{a}\ne \mathrm{b})>1$, then the value of $(\mathrm{a}+\mathrm{b})$ is:

At a bangle shop, when the shopkeeper tries to display all the bangles in the form of a square, he is left with $38$ bangles that cannot be accommodated in the square arrangement. If he wants to increase the size of the square by one unit, he needs to buy $25$ more bangles to complete the square arrangement.

However, when he arranges the bangles, he keeps all the bangles adjacent to each other without any overlapping. What is the actual number of bangles in his shop?