In school days, we used to find squares, square roots, cube roots with long formulated methods, but when you are going to sit in competitive exams, those basics don’t work for you. Here you need tips and tricks to solve the mathematical problems that can fasten your calculation. Let’s start with squaring tricks…
Squaring Tricks
Before going further, first of all, learn squares 1 to 30 and make it on your tips to speed up your squaring. Now when you start squaring
Always Remember:
- Category I - Squaring from 32^{2} to 99^{2} – Results will be Four Digit Long.
- Category II - Squaring from 100^{2} to 316^{2} – Results will be Five Digit Long.
- Category III - Squaring from 317^{2} to 999^{2} – Results will be Six Digit Long.
4 simple methods of Squaring:
- Squares Near 50 (Base 25- It come by squaring 5^{2}=25)
- Squares Near 100
- Split Method
- A B Formulas
Squaring Near 50 and 100 are again divided furthur into two categories as shown below:
Square Near 50
- Square Less< 50
- Step I: Check the category - 46 is under Category I resulting Four Digit Long answer.
- Step II: You get 46 near 50 by subtracting 50-4=46 [Take Subtracting digit as main digit]
- Step III: Take Base 25 and subtract main digit to get first two digits of the answer 25-4=21 [Subtracting digit will be subtracted in base 25]
- Step 1V: Square main integer to get the last digits of answer 4^{2} = 16
- Step I: Check the category – 39 is under Category I resulting Four Digit Long answer.
- Step II: You get 39 near 50 by subtracting 50-11=39 [Take Subtracting digit as main digit]
- Step III:Take Base 25 and subtract main digit to get first two digits of the answer 25-11=14
- Step 1V:Square main integer to get the last digits of answer 11^{2} = 121
- Step V:To get the four digit long answer add both the Step III and Step IV results as:
- Square Greater >50
- Step I: Check the category - 56 is under Category I resulting Four Digit Long answer.
- Step II: You get 56 near 50 by adding 50+6=56 [Take Adding digit as main digit]
- Step III: Take Base 25 and add the main digit to get first two digits of the answer 25+6=31 [Adding digit will be added in base 25]
- Step 1V: Square main digit to get the last digits of answer 6^{2} = 36
Take an example:
Question 1: Find the Square of 46:
Question 2: Find the square of 39
Take an example:
Question1: Find the Square of 56:
Question2: Find the Square of 63:
- Step I: Check the category - 63 is under Category I resulting Four Digit Long answer
- Step II: You get 63 near 50 by adding 50+13=63 [Take Adding digit as main digit]
- Step III:Take Base 25 and add main digit to get first two digits of the answer 25+13=38
- Step 1V: Square main digit to get the last digits of answer 13^{2} = 169
- Step V: To get the four digit long answer add both the Step III and Step IV results as:
Square Near 100
- Square Less< 100
- Step I: Check the category – 97 is under Category I resulting Four Digit Long answer.
- Step II: You get 97 near 100 by subtracting 100-3=97 [Take Subtracting digit as main digit]
- Step III: Take number whose square is to find and subtract from main digit to get first two digits of the answer 97-3=94
- Step 1V: Square main digit to get the last digits of answer 3^{2} = 9
Take an example:
Question1: Find the Square of 97:
Question2: Find the Square of 88:
- Step I: Check the category – 88 is under Category I resulting Four Digit Long answer
- Step II: You get 88 near 100 by subtracting 100-12=88 [Take Subtracting digit as main digit]
- Step III: Take digit whose square is to find and subtract from main digit to get first two digits of the answer 88-12=76
- Step 1V: Square main digit to get the last digits of answer 12^{2} = 144
- Step V:To get the four digit long answer add both the Step III and Step IV results as:
Take an example:
Question1: Find the Square of 104:
- Step I: Check the category – 104 is under Category II resulting Five Digit Long answer.
- Step II: : You get 104 near 100 by adding 100+4=104 [Take Adding digit as main digit]
- Step III: Take main digit and double it as 4+4=8 (add) and then add to base 100 to get first two digits of the answer 100+8=108
- Step 1V: Square main digit to get the last digits of answer 4^{2}=16
Question2: Find the Square of 109:
- Step I: Check the category – 109 is under Category II resulting Five Digit Long answer
- Step II: : You get 109 near 100 by adding 100+9=109 [Take Adding digit as main digit]
- Step III: Take main digit and double it as 9+9=18 (add) and then add to base 100 to get first two digits of the answer 100+18=118
- Step 1V:Square main digit to get the last digits of answer 9^{2} =81
Question3: Find the Square of 123:
- Step I: Check the category – 123 is under Category II resulting Five Digit Long answer
- Step II: : You get 123 near 100 by adding 100+23=123 [Take Adding digit as main digit]
- Step III: Take main digit and double it as 23+23=46 (add) and then add to base 100 to get first two digits of the answer 100+46=146
- Step 1V:Square main digit to get the last digits of answer 23^{2} =529
- Step V:To get the five digit long answer add both the Step III and Step IV results as:
Split method:
Take an example:
Question1: Find the Square of 25:
- Step I: Split 25 as 20 + 5
- Step II: You will get (20 + 5) x (20 + 5)
- Step III: Then Multiply to get the result as:
= (20 + 5) x (20 + 5)
= (20 x 20) + (20 x 5) + (5 x 20) + (5 x 5)
= 400 + 100 +100 +25
- Result= 6 2 5
Question2: Find the Square of 625:
- Step I: : Split 625 as 600 + 20 + 5
- Step II: You will get (600 + 20 + 5) x (600 + 20 + 5)
- Step III: Then Multiply to get the result as:
= (600 + 20 + 5) x (600 + 20 + 5)
= (600 x 600) + (600 x 20) + (600 x 5) + (20 x 600) + (20 x 20) + (20 x 5) + (5 x 600) + (5 x 20) + (5 x 5)
= 360000 + 12000 + 3000 + 12000 + 400 + 100 + 3000 + 100 + 25
- Result = 3 9 0 6 2 5
A B Formulas
Take an example:
Question1: Find the Square of 25:
- Step I:Split as (20 + 5)^{2 }
- Step II: Put in formula (a+ b)^{2} = a^{2}+ b^{2} + 2ab
= (20 + 5 )^{2}
= 20^{ 2} + 5^{2} + 2 x 20 x 5
= 400 + 25 + 200
- Result= 6 2 5
Question2: Find the Square of 16:
- Step I:Split as (10 + 6)^{2}
- Step II: Put in formula (a+ b)^{2} = a^{2}+ b^{2} + 2ab
= (10 + 6 )^{2}
= 10^{ 2} + 6^{2} + 2 x 10 x 6
= 100 + 36 + 120
- Result= 2 5 6