SHORTCUTS FOR SQUARING

In this post we are providing you some basic SHORTCUTS FOR SQUARING NUMBERS which will be useful to you while solving simplification questions or any other questions which involve squaring of number. These Shortcuts for squaring numbers will be helpful and will save a lot of your time in exam. You just need to practice. It is more advisable to learn squares of the numbers from 1 to 25 by heart. It would be very helpful for solving the questions. Below, we have discussed each and every step in detail to help you.If you know more better methods, do share with us in the comments section.

SHORTCUTS FOR SQUARING

• Squaring of a number whose last digit is 1
(31)2

Step1:Write the square of the previous number
(30)2 = 900
Step2:Now add the previous number and the number whose square is being asked
30+31=61
Step3: Now add Step1 and Step 2
900+61= 961

NOTE : If the unit digit of a number is 1 than the unit digit of its square is always 1.

• Squaring of a number whose last digit is 9
(29)2

Step1:Write the square of the next number.
(30)2 =900
Step2: Now Add the number whose square is being asked and the next number.
29+30=59
Step3:Now subtract step1 from step2
900-59 = 841

NOTE : If the unit digit of a number is 9 than the unit digit of its square is always 1.

• Squaring of a number whose last digit is 2 or 8
• Use this formula for Squaring of a number whose last digit is 2
(x-2)2 + 2(x + (x-2)) = a

Example :(42)2
(40)2+ 2(42 + 40)= 1600 + 2 X 82
= 1600 + 164
= 1764

• Use this formula for Squaring of a number whose last digit is 8
(x+2)2 – 2(x + (x+2)) = a

Example : (48)2
(50)2 – 2(48+50) = 2500 – 2 X 98
= 2500 – 196
= 2304

NOTE : If the unit digit of a number is 2 or 8 than the unit digit of its square is always 4.

• Squaring of a number whose last digit is 5
(35)2

Step1:Unit digit is 5 , (5)2= 25
Step2: Now Add 1 to the ten’s digit and multiply it with the ten’s digit .
3 X (3+1) = 3 X 4
= 12
Step3: Place the step 2 first and step 1 second
Therefore the answer will be 1225

NOTE : If the unit digit of a number is 5 than the unit digit of its square is always 5.

• Squaring of a number whose last digit is 3 or 7
• Use this formula for Squaring of a number whose last digit is 3
(x-3)2 + 3(x + (x-3)) = a

Example :(43)2
(40)2+ 3(43 + 40)= 1600 + 3 X 83
= 1600 + 249
= 1849

• Use this formula for Squaring of a number whose last digit is 7
(x+3)2 – 3(x + (x+3)) = a

Example : (47)2
(50)2 – 3(47+50) = 2500 – 3 X 97
= 2500 – 291
= 2209

NOTE : If the unit digit of a number is 3 or 7 than the unit digit of its square is always 9.

• Squaring of a number whose last digit is 4 or 6
• Use this formula for Squaring of a number whose last digit is 4
(x-4)2 + 4(x + (x-4)) = a

Example :(44)2
(40)2+ 4(44 + 40)= 1600 + 4 X 84
= 1600 + 336
= 1936

• Use this formula for Squaring of a number whose last digit is 6
(x+4)2 – 4(x + (x+4)) = a

Example : (46)2
(50)2 – 4(46 + 50) = 2500 – 4 X 96
= 2500 – 384
= 2116

NOTE : If the unit digit of a number is 4 or 6 than the unit digit of its square is always 6.