We all know that squaring any number is to multiply the number by itself. Even though it is a type of multiplication, let us see what is special about it. As usual we can learn a specific method for numbers near the base.
First let us see a method to find the square of a number near a base. The numbers which are near the base like 10, 100, 1000 etc. are always easy for calculations. First let us find the square of numbers which are greater than the base numbers.
Let us see this with an example - find the square of 13.
First note down the base is 10.
Next to note is, 13 is 3 more than the base. So let us call it the increment. This increment has a lot of work to do.
Add the given number with the increment and that is the first part of the answer. i.e, 13 + 3 = 16.
Square the increment which gives the second part of the answer. i.e., 32=9
So the answer is 169
132 +3 (Base is 10)
13+3 32
16 9
Now this one is very easy for most of us. If it is true let us use this and do another problem. Let us find 232.
Let us take 10 as the base and do the problem.
Then 23 is 13 more than the base. So increment is 13.
So our first task is to add the increment with the number to get the first part of the answer. So 23 +13= 36 will be the first part of the answer.
Now to square the increment which we have already done in our first example as 132 = 169.
So we get 36 and 169 as the two parts of the answers, but writing this as it is will be a wrong answer.
Remember our base is 10 so only one digit is allowed in the second part of the answer.
So in 169 put only 9 in the unit’s place and add the remaining to the first part of the answer.
So (36 + 16) and 9 = 529 is the answer.
232 13 (Base is 10)
23+13132
3616 9
36 + 16 9
529 So the answer is 529.
Now let us see another example, 1122.
For 1122 the base is 100 and the increment is 12.
1122 12 (100)
112 +12122
124144 (since the base
is 100, retain 44 and carry over 1)
12544 so the answer is
12544.
Now you can try,
162, 212, 172, 1042, 1082