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 49,191,931? It is this number: 49191931. 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 49,191,931?
Answer: 1
Step 3:
So now we know the digital root of 49,191,931 is 1. Is 1 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
Answer: YES, 1 is in the list of digital roots that are always perfect squares. We can conclude that 49,191,931 could be a perfect square!
Factoring
OK, so now we know that 49,191,931 could be a perfect square. We have to find the factors of the number to be sure.
Here are all of the factors of 49,191,931:
Number | 49,191,929 | 49,191,930 | 49,191,932 | 49,191,933 |
Perfect Square? | no | no | no | no |