You can find square of any number in the world with this method.

Let’s say the number is two digit number. i.e. AB.
So B is units digit and A is tens digit.

Step 1: Find Square of B

Step 2: Find 2×A×B

Step 3: Find Square of A


Let’s take an example.

We want to find square of 37.

Step 1: Find square of 7.

        Square of 7 = 49.

        So write 9 in the answer and 4 as carry to the second step.   

 

       Square Shortcut Method

Step 2: Find 2×(3×7)

        2 × (3 × 7) = 42.
        42 + 4(Carry) = 46.
        Write 6 in the answer and 4 as a carry to the third step.

        Square Shortcut Method

Step 3: Find square of 3

        Square of 3 = 9
        9 + 4(Carry) = 13.
        Write 13 in the answer.

        Square Shortcut Method

        So the answer is 1369.

 

Now, If the number is of three digit i.e. ABC
Here C is unit’s digit, B is ten’s digit and A is hundredth digit.

Step 1: Find Square of C

Step 2: Find 2 × (B × C)

Step 3: Find  2 × (A × C) + B2

(NOTE: You may observe that in odd number of digit case,  we are multiplying end two digits with 2 (here: A and C) and squaring single digit (here B).

Step 4: Find 2 × (A × B)

(NOTE: You may observe that whenever there are double digits, we are multiplying it with 2. And whenever there is single digit, we are squaring it.)

Step 5: Find square of A
        (NOTE: Here is single digit, so we are squaring it.)


Let’s take an example.

Find square of 456.

Step 1: Find square of 6.

        Square of 6 = 36.

       So write 6 in the answer and 3 as a carry to the second step.

        Square Shortcut Method

Step 2: Find 2 × (5 × 6)

        2 × (5 × 6) = 60
        60 + 3(Carry) = 63
        Write 3 in the answer and 6 as a carry to the third step.

       Square Shortcut Method

Step 3: Find  2 × (4 × 6) + 52

        2 × (4 × 6) + 52 = 73
        73 + 6(Carry) = 79
        Write 9 in the answer and 7 as a carry to the fourth step.

        Square Shortcut Method

Step 4: Find 2 × (4 × 5)

        2 × (4 × 5) = 40
        40 + 7 = 47
        Write 7 in the answer and 4 as a carry to the fifth step.

        Square Shortcut Method

Step 5: Find square of 4

        Square of 4 = 16
        16 + 4(Carry) = 20
        Write 20 in the answer.
       

        Square Shortcut Method

So 4562 = 207936.

 

Now, If the number is of four digit i.e. ABCD
Here D is unit’s digit, C is ten’s digit, B is hundredth digit and A is thousands digit.

Step 1: Find Square of D

Step 2: Find 2 × (C × D)

Step 3: Find  2 × (B × D) + C2

(NOTE: You may observe that in odd number of digit case,  we are multiplying end two digits with 2 (here: B and D) and squaring single remaining digit (here C).

Step 4: Find 2 × (A × D) + 2 × (B × C)

(NOTE: You may observe that where ever there is even digits, we are multiplying end two digits with 2 + remaining two digits with 2.)

Step 5: Find  2 × (A × C) + B2

(NOTE: You may observe that in odd number of digit case,  we are multiplying end two digits with 2 (here: A and C) and squaring single remaining digit (here B).

Step 6: Find 2 × (A × B)

(NOTE: You may observe that here even digits so we are multiplying them with 2, and no remaining digits so we are not adding anything.)

Step 7: Find square of A

 

Let’s take an example.

Find square of 1234

Step 1: Find Square of 4

        Square of 4 = 16
       So write 6 in the answer and 1 as a carry to the second step.

       Square Shortcut Method  

Step 2: Find 2 × (3 × 4)

        2 × (3 × 4) = 24
        24 + 1(Carry) = 25
        Write 5 in the answer and 2 as a carry to the third step

        Square Shortcut Method

Step 3: Find  2 × (2 × 4) + 32

        2 × (2 × 4) + 32 = 25
        25 + 2(Carry) = 27
       Write 7 in the answer and 2 as a carry to the fourth step.

        Square Shortcut Method

Step 4: Find 2 × (1 × 4) + 2 × (2 × 3)

        2 × (1 × 4) + 2 × (2 × 3) = 20
        20 + 2(Carry) = 22
        Write 2 in the answer and 2 as a carry to the fifth step.

        Square Shortcut Method

Step 5: Find  2 × (1 × 3) + 22

        2 × (1 × 3) + 22 = 10
        10 + 2(Carry) = 12
        Write 2 in the answer and 1 as carry to the sixth step.

        Square Shortcut Method

Step 6: Find 2 × (1 × 2)

        2 × (1 × 2) = 4
        4 + 1(Carry) = 5
        Write 5 in the answer

        Shortcut Method For Square

Step 7: Find square of 1

        Square of 1 = 1
        There is no carry so write 1 in the answer.

        Square Shortcut Method

So, 12342 = 1522756