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...
What is the last number of 542,159? It is this number: 542159. 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.
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 542,159?
So now we know the digital root of 542,159 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 542,159 IS NOT a perfect square and we don't need to factor!