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:

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

__11__3 or

__11__7

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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