Maths for SSC Exam

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.