Question

by splitting into prime factors find the square root of
7056​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Step 1:

What is the last number of 7,056? It is this number: 7056. The answer is 6. Is 6 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: NO, 6 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:

7 + 0 + 5 + 6 = 18

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

1 + 8 = 9

What is the digital root of number 7,056?

Answer: 9

Step 3:

So now we know the digital root of 7,056 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?

Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 7,056 could be a perfect square!

Factoring

OK, so now we know that 7,056 could be a perfect square. We have to find the factors of the number to be sure.

Here are all of the factors of 7,056:

1 x 7,0562 x 3,5283 x 2,3524 x 1,7646 x 1,1767 x 1,0088 x 8829 x 78412 x 58814 x 50416 x 44118 x 39221 x 33624 x 29428 x 25236 x 19642 x 16848 x 14749 x 14456 x 12663 x 11272 x 9884 x 84

Whoa! That is a lot of factors!

Highlighted in orange above is the factor combination that makes 7,056 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: 84 x 84 =7056