**MATHS TRICK-19**

Here is the some examples & detailed explanatory tricks to find the square of a number

1. For 11 to 19

Let's find the square using an example:

14 : It is 4 more than 10 (14-10=4) So the square=14+4 | 4's Sq = 18 | 16 = 18+1 | 6 = 196

(Note: If after | is exceeds one digit then right-most digit will be there but other will be added before | )

2. For 20 to 29

23’Sq = 2 X (23+3) | 3’Sq= 2 X (26) | 9 = 52 | 9 = 529

3. For 30 to 39

37’Sq = 3 X (37+7) | 7’Sq= 3 X (44) | 49 = 132 | 49 =132+4 | 9 = 136 | 9 = 1369

3. For 40 to 49

49’Sq = 4 X (49+9) | 9’Sq= 4 X (58) | 81 = 232 | 81 =232 + 8 | 1 = 240 | 1 =2401

(Note: If after | is exceeds one digit then right-most digit will be there but other will be added before | )

**Detailed Explanations:-**

Let us first find square of 11 using formula:

11’square=11+1 | 1's square=12 | 1=121.

The formula is self explanatory. However, let me explain it in detail for more clarification.

• The slash is used just as a operator.

• Our operating zone is 10 X 1 or simply 10.

• 11 is more than 10.

• We add 1 to 11to make 12.

• The number of digits after the slash can be only one.

• If the number of digits after the slash exceeds one, then we place only the rightmost digit on the extreme right after the slash, and the remaining gets added to the number on the left hand side of the slash.

• Now have a look at few more examples for better understanding.

12’square=12+2 | 2’square=14 | 4=144

13’square=13+3 | 3’square=16 | 9=169.

14’square=14+4 | 4’square=18 | 16 (Apply step no 6 here) 18 | 16=18+1 | 6=196.

You can work like this up to 19’square.But for 20 formula is slightly change.

The slight Change in formula as follows:

21’square=2 X (21+1) | 1’square= 2 X (22) | 1=44 | 1=441.

This change is because now we are operating in the 10 X 2 Zone. Similarly we can calculate Square of 31 but with slight change as follows:

31’Square=3 X (31+1) | 1’s square= 3 X (32) | 1=96 | 1=961.

By these methods explained you can easily calculate and memorize the squares of numbers up to 99 with out much hassle.

**Steps to calculate square of a three digit number:**

• Consider number 121 to find square.

• Separate digits as 12 & 1.

• Now do Square of unit digit number i.e. 1’square=1, so our unit digit number is 1 now in this case.

• Then multiply both separated Digits which are earlier separated ie.12 & 1

• =12 X 1=12

• Now double the result of multiplication i.e. Double of 12= 24. And place it left after unit digit number i.e. 2 41.( 2 is Carry)

• Separate carry 2 then

• Now At last square 12 i.e. 12’square=144 and add earlier Carry to it.

• So we get 144+2(carry)=146

• Finally we obtained Square as 14641..

Let us have a look at one more example.

151’square:

• 1’s square=1.

• 2 x (15 x 1) = 3 0 (Double of 15 and 1 and 3 is carry now.)

• Now 15’square=225+earlier carry i.e.3=228

• So Final Answer is 22801

Page Source URL : VEDIC MATHEMATICS