Question

show that 3675 is not a perfect square

Answer 1

Let's try it...


Step 1:

What is the last number of 3,675? It is this number: 3675. The answer is 5. Is 5 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: NO, 5 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:

Split the number up and add each digit together:


3 + 6 + 7 + 5 = 21


If the answer is more than one digit, you would add each digit of the answer together again:

2 + 1 = 3


What is the digital root of number 3,675?

Answer: 3


Step 3:

So now we know the digital root of 3,675 is 3. Is 3 in the list of digital roots that are always a square root (1, 4, 7 or 9)?

Answer: NO, 3 is not in the list of digital roots that are always perfect squares. We can conclude that 3,675 IS NOT a perfect square and we don't need to factor!