is 16000 is perfect square by prime factorisation
Answers
Try these steps first:
A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.
Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you're lost, don't worry, we'll go over each step in more detail below.
All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.
Let's try it...
Step 1:
What is the last number of 16,000? It is this number: 16000. 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 + 6 + 0 + 0 + 0 = 7
What is the digital root of number 16,000?
Answer: 7
Step 3:
So now we know the digital root of 16,000 is 7. Is 7 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
Answer: YES, 7 is in the list of digital roots that are always perfect squares. We can conclude that 16,000 could be a perfect square!
Factoring
OK, so now we know that 16,000 could be a perfect square. We have to find the factors of the number to be sure.
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 16,000.
That means 16,000 is NOT a perfect square.
Answer:
factorisationis 16000 is perfect square by prime factorisation