Is 8820 a triangular number? (Is 8820 a triangle?)

Is 8820 a triangular number?

Here we will define and determine if 8820 is a triangular number, also known as a triangle number. First, note that an equilateral triangle is a triangle where the length of the three sides are the same, and the three internal angles of the triangle are 60 degrees. An equilateral triangle can look like this:

Take notice of the symmetry of the dots inside the triangle above. Each side of the triangle has the same number of dots, and one dot is added to each row of dots.

8820 is a triangular number if we can arrange all 8820 dots or objects in perfect symmetry to make an equilateral triangle. To determine if a number (n) is a triangular number, the following equation must be true:

√(8 × n) +1 = Integer

When we enter 8820 for n in our formula, we get the following result:

√(8 × 8820) +1 ≈ 265.6332

265.6332 is not an integer (whole number), therefore the answer to "Is 8820 a triangular number?" is as follows:

8820 = Not a triangular number

Since 8820 is not a triangular number, you cannot use 8820 objects or dots to create a symetric equilateral triangle similar to the one pictured above on this page.

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