x
{\displaystyle x}
in the tens place, simply calculate
x
(
x
+
1
)
{\displaystyle x(x+1)}
, then append 25 to the end of this product.
Squaring Numbers Without a Calculator
Separate 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.
Set up the formula x ( x + 1 ) {\displaystyle x(x+1)} x(x+1). Let x {\displaystyle x} x equal the number being squared, excluding the 5 digit in the ones place. Plug this number into the formula. For example, if you are calculating 65 2 {\displaystyle 65^{2}} 65^{{2}}, x = 6 {\displaystyle x=6} x=6. Set up the formula as 6 ( 6 + 1 ) {\displaystyle 6(6+1)} 6(6+1), since 6 is the number you separated from the 5. If you are calculating 115 2 {\displaystyle 115^{2}} 115^{{2}}, x = 11 {\displaystyle x=11} x=11. Set up the formula as 11 ( 11 + 1 ) {\displaystyle 11(11+1)} 11(11+1), since 11 is the number you separated from the 5.
Multiply the two values together. First, find the sum in parentheses. For example: 6 ( 6 + 1 ) = 6 ( 7 ) = 42 {\displaystyle 6(6+1)=6(7)=42} 6(6+1)=6(7)=42. For example: 11 ( 11 + 1 ) = 11 ( 12 ) = 132 {\displaystyle 11(11+1)=11(12)=132} 11(11+1)=11(12)=132.
Append 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. For example: 6 ( 7 ) = 42 {\displaystyle 6(7)=42} 6(7)=42 65 2 = 4225 {\displaystyle 65^{2}=4225} 65^{{2}}=4225 For example: 11 ( 12 ) = 132 {\displaystyle 11(12)=132} 11(12)=132 115 2 = 13 , 225 {\displaystyle 115^{2}=13,225} 115^{{2}}=13,225
Squaring Numbers Using a Calculator
Understand 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.
Multiply 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 95 2 {\displaystyle 95^{2}} 95^{{2}} on a basic calculator, you would type the following sequence: 95 {\displaystyle 95} 95 × {\displaystyle \times } \times 95 {\displaystyle 95} 95 = {\displaystyle =} =You should see a result of 9025 {\displaystyle 9025} 9025.
Use the x 2 {\displaystyle x^{2}} x^{{2}} 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 x 2 {\displaystyle x^{2}} x^{{2}}. Hitting this key will give you the square of a number. To use it, type in the number being squared, then hit the x 2 {\displaystyle x^{2}} x^{{2}} key. For example, to calculate 75 2 {\displaystyle 75^{2}} 75^{{2}} on a scientific calculator, you would type 75 , x 2 {\displaystyle 75,x^{2}} 75,x^{{2}}. You should see a result of 5625 {\displaystyle 5625} 5625.
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