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You can square numbers ending in 5 the same way you square other numbers. A quick way to square any number is by using a calculator; however, when you are squaring a twodigit number ending in 5, you can use an easy method without the aid of a calculator. For a twodigit number with the digit in the tens place, simply calculate , then append 25 to the end of this product.
Steps
Method 1
Method 1 of 2:Squaring Numbers Without a Calculator
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1Separate the 5 from the rest of the number. You want to create two numbers: 5, and the number created by all the remaining digits in the number. This only applies to the 5 in the ones place, and not to other 5s that might appear elsewhere in the number.
 For example, if you are squaring 65, you would create the number 6, and the number 5.
 If you are squaring 115, you would create the number 11, and the number 5.

2Set up the formula . Let equal the number being squared, excluding the 5 digit in the ones place.^{[1] X Research source } Plug this number into the formula.
 For example, if you are calculating , . Set up the formula as , since 6 is the number you separated from the 5.
 If you are calculating , . Set up the formula as , since 11 is the number you separated from the 5.
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3Multiply the two values together. First, find the sum in parentheses.^{[2] X Research source }
 For example: .
 For example: .

4Append 25 to the end of the product. The result of any squared number ending in 5 will end in 25. Adding 25 to the end of the product you found previously gives you the result of squaring the original number.^{[3] X Research source }
 For example:
 For example:
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Method 2
Method 2 of 2:Squaring Numbers Using a Calculator
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1Understand what it means to square a number. Squaring a number means to raise it to the power of 2. To square a number, you simply multiply the number by itself.^{[4] X Research source }

2Multiply using a basic calculator. A basic calculator is a calculator that only has functions for the most basic operations, such as multiplying and dividing. This is the type of calculator you might use in elementary school. To find the square of a number using a basic calculator, type in the number, then the multiplication sign, then the number again, then the equal sign.
 For example, to calculate on a basic calculator, you would type the following sequence:
You should see a result of .
 For example, to calculate on a basic calculator, you would type the following sequence:

3Use the key on a scientific calculator. Scientific calculators are calculators that contain a variety of functions needed in upper level maths. Scientific calculators contain a key labeled . Hitting this key will give you the square of a number. To use it, type in the number being squared, then hit the key.
 For example, to calculate on a scientific calculator, you would type . You should see a result of .
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Community Q&A

QuestionWhen won't this conjecture work?DonaganTop AnswererIt's not a conjecture. It's a rule, and it works with any number ending in 5. However, the point is to be able to square these numbers in your head without using a calculator, and once you get into tripledigit numbers above 115, it's a little hard to use this procedure in your head.
Tips
References
 ↑ https://www.math.hmc.edu/funfacts/ffiles/10003.1.shtml
 ↑ http://www.cuttheknot.org/arithmetic/rapid/Specifics/SquareEndIn5.shtml
 ↑ http://www.quickanddirtytips.com/education/math/5tipsforfastermentalmultiplication
 ↑ http://www.virtualnerd.com/algebra1/algebrafoundations/powerssquareroots/powersexponents/squaringanumber