Q: Is 420,201,998 a Perfect Square?

Why is 420,201,998 not a perfect square?

A perfect square is a number that can be expressed as the product of two equal integers.

The only way to accurately calculate if a number is a perfect square is to find the factors. Before we go through the trouble of finding the factors, there is a quick trick you can use to help determine if you need even need to do the extra work.

Try these steps first:

1. A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.
2. Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you're lost, don't worry, we'll go over each step in more detail below.
3. All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.

Let's try it...

Step 1:

What is the last number of 420,201,998? It is this number: 420201998. The answer is 8. Is 8 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: YES, 8 is in the list of numbers that are never perfect squares. The number 420,201,998 is NOT a perfect square and we can stop here as there is not need to complete the rest of the steps.

More Examples