A perfect square is a number that can be expressed as the product of two equal integers. The only way to accurately calculate if a number is a perfect square is to find the factors. Before we go through the trouble of finding the factors, there is a quick trick you can use to help determine if you need even need to do the extra work. Try these steps first:
Let's try it... Step 1: What is the last number of 709? It is this number: 709. The answer is 9. Is 9 in the list of numbers that are never perfect squares (2, 3, 7 or 8)? Answer: NO, 9 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:
7 + 0 + 9 = 16 If the answer is more than one digit, you would add each digit of the answer together again: 1 + 6 = 7 What is the digital root of number 709? Answer: 7 Step 3: So now we know the digital root of 709 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 709 could be a perfect square! Factoring OK, so now we know that 709 could be a perfect square. We have to find the factors of the number to be sure. Here are all of the factors of 709: 1 x 709 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 709. That means 709 is NOT a perfect square.
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