How to Calculate the Sum of a Number and the Square of Another?

Calculating the sum of a number and the square of another is a straightforward arithmetic operation. Let’s break it down step-by-step.

Step-by-Step Process

1. Identify the Numbers
   First, you need two numbers. Let’s call the first number $a$ and the second number $b$

2. Square the Second Number
   Next, you square the second number $b$. Squaring a number means multiplying the number by itself. The mathematical notation for this is $b^2$. For example, if $b = 3$, then $b^2 = 3 times 3 = 9$

3. Add the Numbers
   Finally, you add the first number $a$ to the square of the second number $b^2$. The formula to represent this operation is:

   $S = a + b^2$

   where $S$ is the sum.

Example Calculation

Let’s go through an example to make this clearer.

Example 1

Suppose $a = 5$ and $b = 4$

1. Square the second number: $4^2 = 16$
2. Add the first number to the squared second number: $5 + 16 = 21$
   So, the sum $S$ is 21.

Example 2

If $a = -2$ and $b = 6$

1. Square the second number: $6^2 = 36$
2. Add the first number to the squared second number: $-2 + 36 = 34$
   So, the sum $S$ is 34.

Real-World Applications

This type of calculation is useful in various real-world scenarios. For instance, in physics, you might need to add a constant value to the square of a velocity to find kinetic energy. In finance, you might use such formulas to calculate compound interest or depreciation values.

Conclusion

To sum up, calculating the sum of a number and the square of another involves three simple steps: identifying the numbers, squaring the second number, and adding the result to the first number. The formula you use is $S = a + b^2$. Mastering this basic arithmetic operation can be useful in both academic settings and everyday life.

Citations

1. 1. Khan Academy – Algebra
2. 2. Math is Fun – Algebra Basics
3. 3. Purplemath – Intro to Algebra