Squaring of a number ending with 5

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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 two-digit number ending in 5, you can use an easy method without the aid of a calculator. For a two-digit number with the digit {\displaystyle x}

 in the tens place, simply calculate {\displaystyle x(x+1)}

, then append 25 to the end of this product.

Set up the formula x(x+1){\displaystyle x(x+1)}

. Let {\displaystyle x}

 equal the number being squared, excluding the 5 digit in the ones place.[1] Plug this number into the formula.

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.

Set up the formula x(x+1){\displaystyle x(x+1)}

x(x+1)

. Let {\displaystyle x}

 equal the number being squared, excluding the 5 digit in the ones place.[1] Plug this number into the formula.

  • For example, if you are calculating {\displaystyle 65^{2}}, {\displaystyle x=6}. Set up the formula as {\displaystyle 6(6+1)}, since 6 is the number you separated from the 5.
  • If you are calculating {\displaystyle 115^{2}}, {\displaystyle x=11}. Set up the formula as {\displaystyle 11(11+1)}, since 11 is the number you separated from the 5.

Multiply the two values together. First, find the sum in parentheses.[2]

  • For example: {\displaystyle 6(6+1)=6(7)=42}.
  • For example: {\displaystyle 11(11+1)=11(12)=132}.


Multiply the two values together.
 First, find the sum in parentheses.[2]

  • For example: {\displaystyle 6(6+1)=6(7)=42}.
  • For example: {\displaystyle 11(11+1)=11(12)=132}

Example 1

Example 2

Example 3

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