1: Find square root by prime factorization
1, 2704
Answers
Answer:
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Answer:
Step 1:
What is the last number of 2,704? It is this number: 2704. The answer is 4. Is 4 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?
Answer: NO, 4 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:
2 + 7 + 0 + 4 = 13
If the answer is more than one digit, you would add each digit of the answer together again:
1 + 3 = 4
What is the digital root of number 2,704?
Answer: 4
Step 3:
So now we know the digital root of 2,704 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 2,704 could be a perfect square!
Factoring
OK, so now we know that 2,704 could be a perfect square. We have to find the factors of the number to be sure.
Here are all of the factors of 2,704:
1 x 2,7042 x 1,3524 x 6768 x 33813 x 20816 x 16926 x 10452 x 52
Highlighted in orange above is the factor combination that makes 2,704 a perfect square. Do you see why? A number can only be a perfect square if the product of two exactly the same numbers is equal to the original number.
Here's the proof: 52 x 52 = 2,704