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 21,054,539? It is this number: 21054539. The answer is 9. Is 9 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?
Answer: NO, 9 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 21,054,539?
Answer: 2
Step 3:
So now we know the digital root of 21,054,539 is 2. Is 2 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
Answer: NO, 2 is not in the list of digital roots that are always perfect squares. We can conclude that 21,054,539 IS NOT a perfect square and we don't need to factor!
Number | 21,054,537 | 21,054,538 | 21,054,540 | 21,054,541 |
Perfect Square? | no | no | no | no |