How to calculate the square of number ending with 5

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Students in their exam can save enormous amount of time solving complex problems if they know how to calculate the square of number ending with 5. This quick technique is very easy to learn and handy to apply Lets say you have a Number n5 (Where n can be any digit) then the square of the number can be calculated in these simple four steps

  1. Extract the trailing 5 and consider the remaining digit as n. E.g You have the number 45 then n=4.
  2. To calculate the square put  n(n+1) E.g n=4(4+1) =20
  3. Put 25 for trailing 5
  4. Concatenating them will give the correct square E.g square of 45=2025

For example calculating square for 35

  • Step 1: Here n=3
  • Step 2: n(n+1) =  3(3+1) =3*4 =12
  • Step 3 : 25 for trailing 5
  • Step 4: Concatenating 12 and 25 will give us 1225 which is the correct answer.

To understand the trick more lets take another example of calculate square for 155

  • Step 1: Here n=15
  • Step 2: n(n+1) =  15(15+1) =15*16 =240
  • Step 3 : 25 for trailing 5
  • Step 4: Concatenating 240 and 25 will give us 24025 which is the correct answer.

However we can use the technique described here where we calculate the square of any number in mind but the trick given above is easier for the case where the number’s ending digit is 5.

For example square of 35 can be calculated as x = 35

  • Step 1 :  y=30
  • Step 2 : z= 5
  • Step 3 : (35+5) *(35-5) + 52 =   40*30+25 =  40 *10 *3 +25
  • breaking up 20=2*10 for easier and quick calculation
    400*3+25 =   1200+25 =  1225 is the correct answer

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