# How To Find Square Root Of A Number In Three Easy Steps

A very important topic in Quantitative Aptitude of IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams is squares and cubes. In our previous post, we learnt what squares are and how to find the square of any number in your head, without any pen and paper. Here, we are going to learn how to find the square root of a given number.

Conventionally, we have been finding square root of a number through the ‘long division method’ that was taught to us in school. Here, we are going to discuss the shortcut to finding square root of a number.

### Importance Of How To Find Square Root Of A Number In Less Time?

Finding square roots of numbers can help you save the much-needed time in competitive exams, such as SSC CGL 2017, SSC CHSL 2017, etc, allowing you to attempt more questions in the limited given amount of time.
Finding whether the given number is a perfect square of not, is a lengthy process. If you have a question from simplifications, where you need to find square root in one of the steps, consider the given number to be a perfect square. ONLY when the question is given under the topic approximations, it may not be a perfect square.

### How To Find Square Root Of A Number In Three Easy Steps

Firstly, you must memorise the squares of numbers from 1 to 30.

We have already learnt that there is a certain pattern seen when it comes to square of any number:

SMART METHOD

### How to find square root of a number in a smart method is a 3-step process

Example 1: Find the √2401
Solution:
Step1: Decide the unit’s place of the result.
2401 ends with 1 = Square root will end with 1 or 9
_ 1 or _ 9
Step2: Leave the last 2 digits and find the immediate perfect square before the remaining number.
The immediate perfect square before 24 = 16, which is 42
That is the number in ten’s place
41 or 49
Step 3: To determine whether the square root of 2401 is 41 or 49
Method 1: Take the number that lies exactly between 41 and 49 and square it.
452 = 2025 (We have learnt earlier how to find square of numbers ending with 5)
2025 < 2401
45 < Square root of 2401
And since
45 < 49
Square root of 2401 is 49
Example 2: Find the √6084
Solution:
Step1: Decide the unit’s place of the result.
6084 ends with 4 = Square root will end with 2 or 8
_2 or _8
Step 2: Leave the last 2 digits and find the immediate perfect square before the remaining number.
The immediate perfect square before 60 = 49, which is 72
72 or 78
Step 3: To determine whether the square root of 6084 is 72 or 78
Method 2: Take squares of numbers 70 and 80, since 72 and 78 lie within the range.
702 = 4900
802 = 6400
Since, 6084 is closer to 6400, the square root must also be closer to 80, which is 78
Square root of 6084 is 78
Example 3: Find the √12769
Solution:
Step 1: Decide the unit’s place of the result.
12769 ends with 9 = Square root will end with 3 or 7
_3 or _7

Step 2: Leave the last 2 digits and find the immediate perfect square before the remaining number.

The immediate perfect square before 127 = 121, which is 112
113 or 117
Step 3: To determine whether the square root of 12769 is 113 or 117
Method 1: Take the number that lies exactly between 113 and 117 and square it.
1152 = 13225
12769 < 13225
And since
113 < 115
Square root of 12769 is 113
Method 2: Take squares of numbers 110 and 120, since 113 and 117 lie within the range.
1102 = 12100
1202 = 14400
Since 12100 is closer to 12769, the square root must also be closer to 110, which is 113

Square root of 12769 is 113

Practice this technique well and ensure that the next time you are asked to find the square root of a perfect square, you don’t spend more than 3 seconds.

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Ahmed saleem1314

We need the saqrue root of number 7584516 plz

Guest
SENDIL

Last number maybe 4(or)6

Guest
Meera

That number’s square root is 2754.

Guest
Navya

How do we find square roots of non perfect square numbers?

Guest
gfjhgjk

They can take the nearest no. i think

Guest
sabari

that is the number in ten’s place which means? plz tell me

Guest
karz

how to find square root of 6

Guest
Vineeshkumar

We have already learnt that there is a certain pattern seen when it comes to a square of any number:
How To Find Square Root the 2nd table

on this table perfect square ends with 9 then square root ends with 3 or 7, not 3 or 6

Guest
sunil

soir pls tell me what is the root for 1935

Guest
Meera

I don’t think so that becomes a square because it is ending with a lot of decimals

Guest
Jj

=16 which is 42. Why is it 42?

Guest
Jj

The immediate perfect square before 24 = 16 which is 42. Why is it 42?

Guest
fds

root of 16 = 4, last digit of root of numbre could be 2

Guest
arun

it’s four square !
not 42.

Guest
dev

perfect step to find square root thank oyu

Guest
Aarushi

How to find difficult roots? Like 4root 15

Guest
Rahul R Sekhar

How to find 11449 sq root

Guest
MayBe

The immediate perfect square before 24 = 16 which is 42. Why is it 42? Please explain in detail

Guest
Priyasha

How to find √7

Guest
P.N.John

What do u mean by immediate perfect square.?