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:
Let's try it...
Step 1:
What is the last number of 23,133,221? It is this number: 23133221. The answer is 1. Is 1 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?
Answer: NO, 1 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:
If the answer is more than one digit, you would add each digit of the answer together again:
What is the digital root of number 23,133,221?
Answer: 8
Step 3:
So now we know the digital root of 23,133,221 is 8. Is 8 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
Answer: NO, 8 is not in the list of digital roots that are always perfect squares. We can conclude that 23,133,221 IS NOT a perfect square and we don't need to factor!
Number | 23,133,219 | 23,133,220 | 23,133,222 | 23,133,223 |
Perfect Square? | no | no | no | no |