Trick to Find Square of Numbers from 51 to 59

I’ll share with you one simple method of finding the square of numbers between 50 and 60. Like many other Vedic Mathematics methods, in this method also, we will get the answer in two parts. Since the numbers are in 50s and square of 50 is 2500, we will just use 25 in our calculations, ignoring the zeros.

  1. To get the first part of the answer, add the digit at the units place to 25 and write the sum
  2. To get the second part, calculate the square of units place digit and write it

It’ll be easier to understand this with an example.

To find the square of 57 –

First part: 25 + digit at units unit in 57 = 25 + 7 = 32

Second part: square of 7 = 49

Combining both the parts – 3249 is the answer.

 

Another way to look at it can explain you the logic behind this technique – 57 can be written as

(50+7)^2

= 50^2 +2*50*7 + 7^2

= 2500 + 100*7 + 7^2

=100*(25+7) + 7^2

You can replace 7 by any other number in unit’s place and get answer for it.

 

Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

18 thoughts to “Trick to Find Square of Numbers from 51 to 59”

  1. to find square of any no btn 100-150
    eg (112)2
    1. double unit and tens digit 124
    2. multiply by 100 124*100=12400
    3. Add (12)2 12400+144=12544
    4. that’s it

  2. to find square of any no btn 50-86
    eg (62)2
    1.62-50=12
    2. 25+12=37
    3. 37*100=3700
    4. 3700 + (12)2=3700+144=3844
    5. square of 62=3844

  3. to find square of any no btn 36-50
    eg (39)2
    1. 50-39=11
    2. 25-11=14
    3. 14*100=1400
    4. 1400 + (11)2=1400+121=1521
    5. square of 39=1521

  4. Square of any two digit number:
    (ab)=(a^2+carry)(2ab+carry)(b^2)
    Note: Always start from right end.
    Example:
    63^2=(6^2)(2*6*3)(3^2)
    =(36+3)(6)(9)
    =3969.
    This way u calculate square of any 2 digit number.

    1. Why 91-99 any number, very easy, read my proverb in Hindi dt 24th of FEb 2012:
      Rule: Add and substract equal number to make a number in tens. Multiply one with another and add square of the number added/substracted

      eg 91^2 = ( 91-1)x (91+1)= (90×92) +1×1 = 8281

      Try with any number. Read Rule again in Hindi:
      ????? ????? ???? ????,
      ?? ?????? ?? ???? ?????
      ?? ???? ?? ???? ?? ???? ???,
      ??? ???? ?? ???? ???? Rule from ” Forget Forgetting” Book

      1. Sir,

        Can u pls tell in english, for those who could’t able to read/understand hindi..
        -Skr

  5. ???? ?? ??? ?? ????: ???? ???? ?? ????? ????? ???? ????,
    ?? ?????? ?? ???? ?????
    ?? ???? ?? ???? ?? ???? ???,
    ??? ???? ?? ???? ????

    ??????: 77 ?? ???? ????? ????
    77-7=70 ? 77+7=84
    77×84=5880 ? ????? 7 ?? ???? ???? 49 ???? ?? ????? 5929 ? ??????? (????? ?????)
    ???: 7 ?? ?????? ? ?????, ???? ?? ???? ????? ?? ??? ??: ” ?????? ??? ?????” ?????? ?? ???? ???? ?? ??????

  6. Cud u plz…tel me thd trick to find the square of the number from 61 to 69 ,from 71 to 79 ,from 81 to 89 nd from 91 to 99

  7. For 41 to 49 we shd remember “15” & “50”.

    To find the square of 42 –

    First part: 15 + digit at units unit in 42 = 15 + 2 = 17

    Second part: square of (50-42) i.e., suare of 8 =64

    Combining both the parts – 1764 is the answer

    1. For squares of 41 to 49, the same logic will be used with a small modification….
      Let us find the square of 46
      Step 1:
      First place square + unit place
      (4×4) + 6 = 16 + 6 = 22
      Step 2:
      Unit place square
      6×6 = 36
      Hence 2236.
      Step 3: (Modification)
      Now to get the answer, multiply unit place with 20 and deduct that number from the number which we got in step 2
      i.e. 2236-(6*20) = 2236-120 = 2116
      Therefore 46×46 = 2116.

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