# How to easily square numbers ending in 5

## How to easily square numbers ending in 5

The following is an easy method to square numbers with a units digit of 5.

The algebra behind this is as follows:

10X+5 should be represent any number with a units digit of 5.

(10X+5)(10X+5)

100X^2 + 100X + 25

(10X (10X+10)) + 25

((10X)*(10X)(X+1)) +25

((10X)*(10X)(X+1)) shows step [3], where the original tens digit (10X) is multiplied by the result of step [2], (10X)(X+1). Step [4] is represented by the last constant of +25 in the above expression.

- Begin with the multiplication of 65*65 or something similar
- Next add one to the tens digit of the number being squared: 6+1=7
- Multiply the result with the original number: 6*7= 42
- Place this number before 25 to get 4225
- This process should work each time

The algebra behind this is as follows:

10X+5 should be represent any number with a units digit of 5.

(10X+5)(10X+5)

100X^2 + 100X + 25

(10X (10X+10)) + 25

((10X)*(10X)(X+1)) +25

((10X)*(10X)(X+1)) shows step [3], where the original tens digit (10X) is multiplied by the result of step [2], (10X)(X+1). Step [4] is represented by the last constant of +25 in the above expression.

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