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Thursday, September 4, 2014

Squaring of Numbers ending in 5 (Five)

Squaring is multiplying a number by itself. Let us have a look at how to square a numbers ending in 5 (five) in a simplest way.

Example 1 : Square of 75

Apart from 5 the number is 7. The number that comes after 7 is 8. We multiply 7 with 8 and write the answer LHS 56. Next, we multiply the last digit (5x5) and put 25 beside it and get our answer as 5625. Thus, 75x75 = 5625.

Example 2 : Square of 115

In the previous example we have solved two digits number. But, the same technique can be extended to numbers of any length. In Example 2, we will try to determine square of a three digit number 115.

Apart from 5 the digits are 1 and 1 i.e. 11. The number that comes after 11 is 12. We multiply 11 with 12 and write the answer LHS 132. We suffix 25 to it and write the final answer as 13225. So, the square of 115 is 13225.

A few more examples are given below:

  • 25x25 = (2x3)|(5x5) = 625
  • 45x45 = (4x5)|(5x5) = 2025
  • 65x65 = (6x7)|(5x5) = 4225
  • 85x85 = (8x9)|(5x5) = 7225
  • 105x105 = (10x11)|(5x5) = 11025
  • 125x125 = (12x13)|(5x5) = 15625

Fact:- LHS will always be 25, in case of squaring numbering ending in 5

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