Question

Show that 500 is not a perfect square

Answer 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.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.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 500? It is this number: 500. The answer is 0. Is 0 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: NO, 0 is not in the list of numbers that are never perfect squares. Let's continue to the next step.


Step 2:

We now need to obtain the digital root of the number. Here's how you do it:

Split the number up and add each digit together:

5 + 0 + 0 = 5



What is the digital root of number 500?

Answer: 5


Step 3:

So now we know the digital root of 500 is 5. Is 5 in the list of digital roots that are always a square root (1, 4, 7 or 9)?

Answer: NO, 5 is not in the list of digital roots that are always perfect squares. We can conclude that 500 IS NOT a perfect square and we don't need to factor!