Square Root Tricks

The Trick To Solve Tricky Square Root Problems

Are you taking extra time than it actually requires to solve complex square root equations? Well, now with the help of square root tricks you can find the square of numbers very easily and with much less time. Tips and tricks always help us to solve mathematical problems easily and swiftly. Therefore, we have it here for you a few helpful tips with which you can find the square root of a given number without any kind of help, especially that of a calculator. Class 8 is the stage we learn about the concept of squares and the square root at full length. To begin with, finding the square root of a number, what we have to know first is if the number is a perfect square or not. And we all know that there are two conditions to find if a number is a perfect square or not.

First, a number will be a perfect square if it ends with 1, 4, 5, 6, and 9. 


Second, a number will never be a perfect square if it ends with 2, 3, 7, and 8. 

These two tips are the most basic tips to find square root but they are not enough. 


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What is Square Root?

The square root of a number is a value that we get when it is multiplied to itself and produces the original number. For example, when 5 is multiplied to itself we get 25. Thus we can say that 5 is a square root value of 25. In the same way, 4 is the square root value of 16, 6 is the square root value of 36, and 77 is the square root value of 49. 


Now, just like a square is a representation of the area of a square that is equal to the side x side, the square root is the representation of the length of the side of a square. 

A square root has a symbol that is denoted as ‘√’. Therefore, we can write square root numbers as √4, √5, √8, √9, etc. 


How to Find Square Root?

Now we have come to the main point. How do we find the square root a number? Finding the square root of numbers such as 4, 9, 16, 25, etc. is the right-hand task. And I’ll tell you why? It is because we all know that from the multiplication table of 1 to 10, the number which is multiplied by itself gives the squares, in a two-digit form. But what if a number is in three-digit or four-digit? Well, then it is considered as difficult to find the root of these numbers. And that is because we fail to remember the table for higher numbers. So why not know the trick behind to determine the root of larger numbers?


Example 1:  Let us consider that we need to find the square root of a large number of 4489.

Step 1: Here, in this number, the unit digit is 9 that means it can be a unit digit of its square root number that is 3 or 7 that is because 32 is 9 & 72 is 49.

Step 2: Now if we consider the first two digits that is 44, it comes between the squares of 6 & 7 because 62 < 44< 72.

Step 3: We can expect that in the ten’s digit of the square root of 4489 is the lowest amidst the two numbers i.e. 6 and we want to find the unit digit of the square root of the number 4489.

Step 4: Now, we would want to find between 63 or 67 is the square root of 4489.

Step 5: Considering the ten’s digit is 6 and the next number is 7, we have to multiply both the numbers like 6 x 7 = 42 and because 42 is less than 44.

Step 6: Square root of 4489 has to be the bigger number between 63 and 67 i.e. 67.

Therefore, \[\sqrt{4489}\] = 67.


Example 2: We can have a look at one more example, the square root of 7056.

Given below is the step by step method:

  • Now, in this number, the unit digit is 6. What all numbers do have the unit digit as 6 on their square roots. Those are 4 t& 6 because 42 is 16 & 62 is 36.

  • Now consider that the first two digits i.e., 70 comes between the squares of 8 & 9 because of 82 < 70 <92.

  • Assume that in the ten’s digit of the square root of the 7056, it is the lowest amidst the two numbers that are 8.

  • So, we have to find the unit digit of the square root of the number 7056. And for that, we have to find between 84 and 86 which one is the square root of 7056.

  • Since the ten’s digit is 8 & the proceeding number is 9, we have to perform multiplication of both the numbers like 8 x 9 = 72 and because 72 is bigger than 70.

  • The square root of 7056 needs to be a lesser number between 84 and 86 that is 84.

Therefore, \[\sqrt{7056}\] = 84.


There are various square roots tricks pdf just like this method, that you can find on the web. Try to find the square roots of large numbers using these tricks, and I bet you will be able to solve an equation within no time.


Given below is a table of square root from numbers 1 to 50. This table will help you to solve the problems based on them very easily.  


Square Root Table From 1 to 50

Number

Square Root Value ( √ )

1

1

2

1.414

3

1.732

4

2

5

2.236

6

2.449

7

2.646

8

2.828

9

3

10

3.162

11

3.317

12

3.464

13

3.606

14

3.742

15

3.873

16

4

17

4.123

18

4.243

19

4.359

20

4.472

21

4.583

22

4.69

23

4.796

24

4.899

25

5

26

5.099

27

5.196

28

5.292

29

5.385

30

5.477

31

5.568

32

5.657

33

5.745

34

5.831

35

5.916

36

6

37

6.083

38

6.164

39

6.245

40

6.325

41

6.403

42

6.481

43

6.557

44

6.633

45

6.708

46

6.782

47

6.856

48

6.928

49

7

50

7.071

FAQ (Frequently Asked Questions)

Question 1) State the Difference Between Square Root and Under Root.

Answer 1) The difference between a square root and an under root can be explained as: An under root can be used for any of the square root, cube root as well as the nth root. In fact, we can say that under root is just another way to express nth root. On the other hand, a square root can only be used for a square root. 


25 under root to the power 2 will be the square root of 25, which is 5. On the other hand, the square root of 25 will be 5.

Question 2) How are Square Root Useful?

Answer 2) Square roots are useful in many ways. In probability theory and statistics, the square root defines a lot of important concepts of standard deviation.  It is extremely useful in the formula for the roots of a quadratic equation. There are other concepts based on square roots such as quadratic fields and rings of quadratic integers that are essential in algebra and also in geometry. Carpenters, engineers, and architects also need a square root when they use Pythagorean Theorem basically to lay the foundation plan or floor plan in order to generate an accurate and square building.