Here we will see the trick using which you can find the square of any number mentally.
Short Trick:
For finding the square of a number we will first see which is the closest number whose square can be easily found. This will be our Base. For Example, if we want to find the square of 11, then the closest number whose square can be found easily is 10. Therefore 10 will be our Base. Similarly if we want to find the square of 26, then the number closest to 26 whose square can be found easily is 25. Therefore 25 will be our base.
Formula:
When the number (N) is 1 greater than or less than Base (B), then square can be found using formula.
(N)2 = (B)2 + 2x(B) + 1 (when number is 1 greater than base)
or
(N)2 = (B)2 – 2x(B) + 1 (when number is 1 less than base)
When the number is 2 greater than or less than Base, then square can be found using,
(N)2 = (B)2 + 4x(B) + 4 (when number is 2 greater than base)
or
(N)2 = (B)2 – 4x(B) + 4 (when number is 2 less than base).
Let’s find square of 81
Solution:
Here, 81 is close to 80. therefore our base will be 80.
Since,
81 is 1 greater than 80, so we will use following formula,
(N)2 = (B)2 + 2x(B) + 1
(81)2 = (80)2 + 2x(80) + 1
= (6400) + 160 + 1
= 6561
Let’s find square 43
Solution:
Here, 43 is close to 45. therefore our base will be 45.
Since, 43 is 2 smaller than 45. therefore we will use following formula,
(N)2 = (B)2 - 4x(B) + 4
(43)2 = (45)2 - 4x(45) + 4
= 2025 - 180 + 4
= 1849