I can tell you with lot of confidence, that you donot often find many questions where you need to obtain the square of a 4-digit number. Squaring a 2 or 3 digit number is probably the most commonly asked question in any competitive examinations. However, obtaining the square of a 4-digit is very similar to obtaining square of a 2 or 3-digit number
Assume a general 4-digit number and call it abcd. Let’s use the criss-cross multiplication to obtain the square of abcd. The steps are illustrated in the following figure:
This can be re-written as shown :
Step 1 : Break the number such that you have a, b, c and d.
Step 2 : Compute a2, b2, c2, d2, ab, ac, ad, bc, bd and cd.
Step 3 : Notice the first row. You have 7 columns. You start with a2, ab, ac and ad. Next, leave bc. Place bd, cd, and d2. That completes the first row.
Step 4 : Now the second row is obtained by repeating the first row elements. We take the middle 5 terms, leaving out the end terms a2 and d2.
Step 5 : The third row, have 3-elements. So you b2 and c2 as the end elements and bc as the middle term.
Step 6 : In the forth row, you just repeat the middle term bc from the third row.
So, far for populating the elements. It might look difficult. However, if you practice the steps on few random 4-digit numbers, you will understand the pattern.
Add up all the elements taking care of the carry-forward in each addition.
Let’s understand the steps with an example. Let’s use this technique to obtain the square of 12342.
The steps are illustrated in the following figure.
Let’s consider another example. Let’s use this technique to obtain the square of 34782. The steps are illustrated in the following figure.
Now, consider an example like 22222. Notice that all the numbers are same. There is a separate article on how to obtain the squares of any number if all the digits are same. You can go through the article here.
Notice, how easy it is to obtain the square of such a big number. Very easy right 🙂
Try to obtain the squares of the following 4-digit numbers:
Please contact me if some point in the tutorial is not clear. I would be glad to help.