Aptitude

Easiest way to find out the square of any number

When a number is multiplied by itself, it is called as the square of the number.

Like 9 x 9 = 9^2 = 81

Squares plays an important role while solving the mathematical question for aptitude for exams like ssc, bank, ibps, railway etc. It might be a good idea to be able to solve mentally (without paper work) the square of 2 digit numbers i.e 1 to 99 or 100  😛

So how to get square of any number between 1 – 100 or 125 in seconds? Do you have to memorize it? Or there is a simpler way to remember these?

Yes indeed! There are short tricks to solve these onto finger tips. Before starting the process I believe you all are memorised the square of 1 to 10 numbers.

So now let’s come to the tricks –

#1. Squaring of any number between 10 – 30 :

Ex 1. (14)^2  ⇒ 14 + 4 ⇒ 18 x 10 = 180

Now add the Square of 4 = 4^2 = +16  ⇒ 180+16 = 196

Explanation :

  • 14 is 4 greater than 10 so add 4 in 14 = 14+4 = 18
  • Now the base of the number is 10 as is exist in between 10 -19. So multiply the above 18 to 10 i.e 18 x 10 = 180
  • Now add the square of 4 = 4^2 = 16 to the 180, 180 + 16 = 196 answer.

Ex 2. (27)^2  => 27 + 7 = 34 x 20 = 680

Now add square of 7 = 7^2 = +49 ⇒ 680 + 49 = 729 answer.

square of any number between 10-30
You can try to find out more square of number lies between 10 – 30.

#2. Squaring of any number between 31 – 50 :

Ex 3. (36)^2 ?

  • Subtract the number from 50. i.e. ⇒ 50 – 36 = 14
  • Again subtract the resultant from 25 i.e.  ⇒ 25 – 14 = 11
  • Now place the square of 14 after 11. i.e. 11_ _ ⇒ +196 ⇒ 1296 answer.

square of any number between 31-50
#3. Squaring of any number between 51 – 75 :

EX 4.  (63)^2 ?

  • Make two parts of the given number including 50+ i.e ⇒63 = 50+13
  • Now add the greater of 50 part to 25 i.e. ⇒ 25 + 13 = 38 _ _
  • Now Put the square of 13 = (13)^2 = 169 next to the above 38_ _
  • Remember the square of any number between 51 -75 have four digit and the add the remaining digit next to the above number.

63^2 = 50 + 13 ⇒ 25 + 13 = 38 _ _

13^2 = 169 ⇒38 _ _ +169 =3969 Answer

square of any number between 31-50

#4. Squaring of any number between 76 – 100 :

Ex 5. (87)^2 ? ⇒100 – 87 = 13 ⇒ 87 – 13 = 74 _ _

Now add (13)^2 = 169 next to 74 _ _ ⇒ 7569 Answer

  • First of all subtract the given number from 100 i.e. ⇒ 100 – 87 = 13
  • Subtract again the above resultant from given number i.e ⇒87 – 13 = 74 _ _
  • Now Put the square of the Resultant 13= 13^2 = 169, next to the 74 _ _ i.e. ⇒ 7569.

square of any number between 51-75
#5. Squaring of any number between 101 – 125 :

Ex 6. (104)^2 ? ⇒ 100 + 04 = 104 ⇒ 104 + 04 = 108 _ _

Now put square of 04 ⇒ (04)^2 = 16 next to the above resultant 108 _ _ ⇒ 10816 Answer

  •   See how much the given number is greater than 100 ⇒ 104 = 100 + 04
  • So add the 04 to the given number ⇒ 104 + 04 = 108 _ _ this will be first part of our answer.
  • Now put square of 04 ⇒ (04)^2 = 16 next to the above resultant 108 _ _ ⇒ 10816 Answer

Ex 7. (113)^2 ? ⇒ 100 + 13 = 113 ⇒ 113 + 13 = 126_ _

Now put square of 13 = 13^2 = 169 next to the 126_ _ ⇒12769 Answer
square of any number between 101-125