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.

**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.

**Step 3:** Find square of 3

Square of 3 = 9

9 + 4(Carry) = 13.

Write 13 in the answer.

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) + B^{2}

(**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.

**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.

**Step 3:** Find 2 × (4 × 6) + 5^{2}

2 × (4 × 6) + 5^{2} = 73

73 + 6(Carry) = 79

Write 9 in the answer and 7 as a carry to the fourth step.

**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.

**Step 5:** Find square of 4

Square of 4 = 16

16 + 4(Carry) = 20

Write 20 in the answer.

So 456^{2} = 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) + C^{2}

(**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) + B^{2}

(**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.

**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

**Step 3:** Find 2 × (2 × 4) + 3^{2}

2 × (2 × 4) + 3^{2} = 25

25 + 2(Carry) = 27

Write 7 in the answer and 2 as a carry to the fourth step.

**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.

**Step 5:** Find 2 × (1 × 3) + 2^{2}

2 × (1 × 3) + 2^{2} = 10

10 + 2(Carry) = 12

Write 2 in the answer and 1 as carry to the sixth step.

**Step 6:** Find 2 × (1 × 2)

2 × (1 × 2) = 4

4 + 1(Carry) = 5

Write 5 in the answer

**Step 7:** Find square of 1

Square of 1 = 1

There is no carry so write 1 in the answer.

So, 1234^{2} = 1522756