If the sum of a number and its square is 272, What is the number?

Let the number be x:

According to the question: 

x + x² = 272

In the questions where quadratic equations are formed, it is always advised to solve the equations with the help of options.

Putting 16 in the equation:

16 + 16² = 272

16 + 256 = 272

272 = 272

As, this option satisfies the equation, thus, is the correct answer. All the other options will not satisfy the given equation.