Math, asked by janhoor136, 10 months ago

1: Find square root by prime factorization
1, 2704​

Answers

Answered by Anonymous
1

Answer:

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Answered by rathod99999
0

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

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