SHORTCUTS FOR SQUARING

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.