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Square of a number ending with 5

31 viewed last edited 1 year ago
Vivekanand Vellanki
0
Here's a technique I saw to square a number ending with 5. Using an example to find 35^2. First write the low 2 digits - this is always 25. Next, multiply 3 (the number in the tenth place) with its successor (4) to get 12. Write 12 before 25 to get 35^2=1225. Similarly, 45^2=2025 - 20=4*5 and 25 is the low 2 digits.How do I prove that this works for all numbers ending with 5?
Mahesh Godavarti
3
Any number ending in 5 can be written as n \times 10 + 5 , where n is any natural number. Therefore, (n \times 10 + 5)^2 = n^2 \times 100 + 2 \times n \times 10 \times 5 + 5^2 = 100 (n^2 + n) + 25 = 100 \times (n)(n+1) + 25 .
Krishna
0
The explanation for your example. What you're saying is quite true: 35x35 = 1225 Why because 35x35 = (40 - 5) x (30 + 5) = 40 x (30 + 5) - 5 x (30 + 5) = (40x30 + 40x5) - (30x5 + 25) = (4x3)x100 + (40-30)x5 - 25 = 12x100 + 50 - 25 = 12x100 + 25 = 1225. This is happening. It is applicable to all numbers which having 5 in units place.
Sangeetha Pulapaka
-1
To find the square of a number which ends with a 5. It is known that the square of the lower digit is always 25. The value of the square of the upper digits can be found by using a formula n(n+1), where n is the upper digit preceding the lower digit 5 and the value of n\geq1. Square of any number can be found this way. Square of 105. Here the upper digit is 10, square of this n(n+1) will be 10*11= 110 which is followed by the number 25 because the last digit ends with a 5, we get the answer 11025. The number 1035. The square of lower digit 5 is written as 25, the value of the square of the upper digits 103 can be found by using n(n+1) = 103*104 = 107122, so the answer is 1071225