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For a number to be a perfect square, the number's square root has to be a whole number. 9 is a perfect square because its square root is a whole number, 3. If the square root of the number is a decimal, then it is not a perfect square. For example, 13 does not divide evenly so it not a perfect square.
to find the square root of a number you can use the guess and check method which is kind of complicated to explain with just words but i will answer soon and try searching for "How to do the Guess and Check Method" on Google.com or Bing.com by Microsoft or Ask.com To find the square root of a number with a calculator you hit the weird division thingy... after the number/ before the number depending on type of calculator.
I'm assuming you're wondering if a number is a perfect square? Well, memorization will help as will guess and check. However, if you feel like doing it all by hand, simplifying the square will help you determine if it is a perfect square. Example: let's figure out if the number 225 is a perfect square. Let's take 225 and factor it. When you factor this number, you want to look at factoring numbers which are a perfect square in and of themselves. So 22 is 4, but that doesn't factor, how about 52 ? 25 will indeed factor, so we have 25*9 (look at that, 9 is also a factor). If we split it up like this, we have sqrt(25*9). We can take the square root of these individually and multiply them together. sqrt(25)*sqrt(9) = 5*3 = 15. Therefore 225 is a perfect square of 15.
What I do is find the square root of that number and then find the square root of the answer. Example: 1,296. Square root of 1,296, which can be done easily on most calculators: 36 Square root of 36: 6 Your answer is 6 If you want to check up on that, go ahead, but 6x6x6x6=1,296
Since a Beprisque is a whole number that is consecutive and between a prime and a square, we look to the squares above 100 to begin our search. 121 is a square, but the the two odd numbers on either side of it (119 and 123) are not prime, so we check the next odd perfect square. (Why would we skip over 144?) 167 is prime and 169 is a square, so 168 is Beprisque, and is the first 3-digit Beprisque.