We define square numbers as numbers that when squared will equal a whole number. Thus, the list of the first square numbers starts with 1, 4, 9, 16, and so on.

What is the sum of the first 13 square numbers, you ask? Here we will give you the formula to calculate the first 13 square numbers and then we will show you how to calculate the first 13 square numbers using the formula.

The formula to calculate the first n square numbers is displayed below:

To calculate the sum of the first 13 square numbers, we enter n = 13 into our formula to get this:

First, calculate each section of the numerator: 13(13 + 1) equals 182 and (2(13) + 1) equals 27. Therefore, the problem above becomes this:

Next, we calculate 182 times 27 which equals 4914. Now our problem looks like this:

Finally, divide the numerator by the denominator to get our answer:

4914 ÷ 6 = 819

**There you go. The sum of the first 13 square numbers is 819.**

You may also be interested to know that if you list the first 13 square numbers 1, 2, 9, etc., the 13th square number is 169.

Sum of Square Numbers Calculator

Need the answer to a similar problem? Get the first n square numbers here.

What is the sum of the first 14 square numbers?

Here is the next math problem on our list that we have explained and calculated for you.

Copyright | Privacy Policy | Disclaimer | Contact