How To Find Squares Of Numbers Easily For Bank Exams

In this series, you are going to learn the tips and tricks to solve math problems related to squares in bank exams. Not only are we going to discuss the basic concepts like how to find square, but we would also show you the smart methods to do some speed math.

We all understand that apart from accuracy, speed also plays an important role in all competitive exams, especially the bank exams. In a subject like Quantitative Aptitude, in order to solve the maximum number of questions in the given time limit, you should be able to calculate fast. Here, we would go through some techniques and shortcuts to finding squares of numbers that will help you cut down on the time spent on each question when appearing for any bank exam.

What Is Square Of x?

How to find square is an important concept that frequently is seen in all bank exams.
Square of x is nothing but the number x multiplied with itself.

Things To Remember To Find Square Of A Number

It is very important that we find the square of the given number with minimum time spent. If you want to perfect finding squares of a given number, you must first learn squares of numbers from 1 to 30.
An interesting thing to notice is how the units place for the square changes as the units place for the number changes. This would be helpful in finding out square roots.
1. When a number ends with 1, the square root either ends with 1 or 9.
Square root of 81 is 9
Square root of 441 is 21
2. When a number ends with 4, the square root either ends with 2 or 8.
Square root of 64 is 8
Square root of 324 is 18
3. When a number ends with 9, the square root either ends with 3 or 7.
Square root of 289 is 17
Square root of 169 is 13
4. When a number ends with 6, the square root either ends with 4 or 6.
Square root of 196 is 14
Square root of 676 is 26
5. When a number ends with 25, the square root ends with 5.
Square root of 225 is 15
Square root of 625 is 25
6. When a number ends with 00, the square root ends with 0.Square root of 400 is 20
Square root of 900 is 30

How To Find Squares Of Numbers More Than 30

Example 1: Find 632
Solution:
Example 2: Find 722
Solution:

Example 3: Find 422
Solution:
Here is how finding square of a number in the Smart Method saves time:
1. The first number (a2) is always 2500, which is always fixed.
2. The second term (2ab) is b*100
3. The third term is b2

Example 1: Find 842
Solution:
842 = (100 - 16)2
Applying the algebraic expansion of (a - b)2 = a2 - 2 ab + b2
Here: a = 100, b = 16
84= 10000 - 3200 + 256
Step 1: The first number (a2) is always 10000
84= 10000 - 3200 + 256
Step 2: Double b and add 2 zeros to b (2 ab)
84= 10000 - 3200 + 256
Step 3: b(Since we have memorized squares of all numbers upto 30)
Hence, 842 = 7056

Example 2: Find 922
Solution:
922 = (100 - 8)2
Applying the algebraic expansion of (a - b)2 = a2 - 2 ab + b2
Here, a = 100, b = 8
92= 10000 - 1600 + 64
Hence, 922 = 8464

For numbers from 130 onwards, the base is taken as 150, 200, 250 and likewise. If you have a fair understanding of what to take as the base, it gets easier to find squares of bigger numbers.
We know the following;
52= 25
152 = 225
252 = 625
And we also that the square of a number ending with 5 is always 25. Therefore, we need to only find digits in the first part of the square.

If you observe the initial digits of the square, it is always the product of the initial digit before 5 in the number itself multiplied by its next integer, as highlighted below.

352 = (3*4)25 = 1225
452 = (4*5)25 = 2025
752 = (7*8)25 = 5625
1252 = (12*13)25 = 15625
1952 = (19*20)25 = 38025
And so on.
This is nothing but the multiplication of complementary numbers.

Read our next post to understand how to find the square root of a perfect square. Ensure to use these smart methods when preparing for competitive exams like SSC CGL 2017. And of course, Keep Practicing!