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 462,307,219? It is this number: 462307219. 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 462,307,219?
Answer: 7
Step 3:
So now we know the digital root of 462,307,219 is 7. Is 7 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
Answer: YES, 7 is in the list of digital roots that are always perfect squares. We can conclude that 462,307,219 could be a perfect square!
Factoring
OK, so now we know that 462,307,219 could be a perfect square. We have to find the factors of the number to be sure.
Here are all of the factors of 462,307,219:
Number | 462,307,217 | 462,307,218 | 462,307,220 | 462,307,221 |
Perfect Square? | no | no | no | no |