Question

3. Show that 1300 is not a perfect square .​

Answer 1

Step 1:

What is the last number of 1,300? It is this number: 1300. The answer is 0. Is 0 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: NO, 0 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:

1 + 3 + 0 + 0 = 4

What is the digital root of number 1,300?

Answer: 4

Step 3:

So now we know the digital root of 1,300 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 1,300 could be a perfect square!

Factoring

OK, so now we know that 1,300 could be a perfect square. We have to find the factors of the number to be sure.

Here are all of the factors of 1,300:

1 x 1,3002 x 6504 x 3255 x 26010 x 13013 x 10020 x 6525 x 5226 x 50

We're looking for a factor combination with equal numbers for X and Y (like 3x3) above. Notice there isn't a equal factor combination,

that when multiplied together, produce the number 1,300. That means 1,300 is NOT a perfect square.