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.

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.

####

Example 1: Find 63

Solution:

Example 2: Find 72

Solution:

Example 3: Find 42

Solution:

Here is how finding square of a number in the Smart Method saves time:

1. The first number (a

2. The second term (2ab) is b*100

3. The third term is b

Example 1: Find 84

Solution:

Example 2: Find 92

Solution:

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.

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!

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.**

### Formula For How To Find Square Of A Number

### 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.

**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**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**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**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**When a number ends with 25, the square root ends with 5.**

Square root of 225 is 15

Square root of 625 is 25**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

^{2}^{}

^{2}Solution:

Example 3: Find 42

^{2}Solution:

1. The first number (a

^{2}) is always 2500, which is always fixed.2. The second term (2ab) is b*100

3. The third term is b

^{2}Example 1: Find 84

^{2}Solution:

84

^{2}= (100 - 16)^{2}
Applying the algebraic expansion of (a - b)

^{2}= a^{2}- 2 ab + b^{2}
Here: a = 100, b = 16

84

^{2 }=__10000__- 3200 + 256**Step 1: The first number (a**

^{2}) is always 10000
84

^{2 }= 10000 -__3200__+ 256**Step 2: Double b and add 2 zeros to b (2 ab)**

84

^{2 }= 10000 - 3200 +__256__**Step 3:**

**b**

^{2 }**(Since we have memorized squares of all numbers upto 30)**

Hence,

**84**^{2}= 7056^{2}Solution:

92

^{2}= (100 - 8)^{2}
Applying the algebraic expansion of (a - b)

^{2}= a^{2}- 2 ab + b^{2}
Here, a = 100, b = 8

92

^{2 }= 10000 - 1600 + 64
Hence,

**92**^{2}= 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;

**5**

^{2}= 25**15**

^{2}= 225**25**

^{2}= 625If 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.

35

^{2}= (**3*4**)25 = 1225
45

75

^{2}= (**4*5**)25 = 202575

^{2}= (**7*8**)25 = 5625
125

195

And so on.^{2}= (**12*13**)25 = 15625195

^{2}= (**19*20**)25 = 38025This 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!

## 0 comments:

## Post a Comment