Sum of Squares Calculator

What is Sum of Squares?

The sum of squares is like adding up the size of each square in a group of numbers. Imagine you have different-sized square tiles, and you want to know how much space they cover altogether. That's what the sum of squares does!

How to Calculate Sum of Squares

To find the sum of squares, we take each number in our list, multiply it by itself (that's squaring it), and then add up all these squared numbers. It's like measuring each square tile and then adding up all their areas.

Formula

We write the sum of squares like this:

\[ \sum_{i=1}^{n} x_i^2 \]

This means:

• \(\sum\) is the big S that means "sum up"
• \(i=1\) means we start with the first number
• \(n\) is how many numbers we have
• \(x_i\) is each number in our list
• \(x_i^2\) means we're squaring each number

Calculation Steps

1. Write down all your numbers
2. Square each number (multiply it by itself)
3. Add up all these squared numbers
4. The total is your sum of squares!

Example and Visual Representation

Let's use an example with the numbers 2, 3, and 4:

2² + 3² + 4² = 4 + 9 + 16 = 29

So, the sum of squares is 29.

Let's show this with a picture:

In this picture, each colored square represents the square of a number. The red square is 2², the green square is 3², and the blue square is 4². When we add up the areas of all these squares, we get our sum of squares, which is 29!