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 314,003,209? It is this number: 314003209. 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 314,003,209?
Answer: 4
Step 3:
So now we know the digital root of 314,003,209 is 4. Is 4 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
Answer: YES, 4 is in the list of digital roots that are always perfect squares. We can conclude that 314,003,209 could be a perfect square!
Factoring
OK, so now we know that 314,003,209 could be a perfect square. We have to find the factors of the number to be sure.
Here are all of the factors of 314,003,209:
Number | 314,003,207 | 314,003,208 | 314,003,210 | 314,003,211 |
Perfect Square? | no | no | no | no |