# HOW TO FIND SQUARE ROOT OF ANY NUMBER-LEARN SERIES

# HOW TO FIND SQUARE ROOT OF ANY NUMBER-LEARN SERIES

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### INTRODUCTION:

Square root of a number is not asked separately in Competitive exams but it is asked in Simplification topic,in which we can score 5 marks in less than 5 minute.Before getting into this topic,let us look in how to square and cube a number,

Now,let us look,how to find square root of a number,

**HOW TO FIND SQUARE ROOT OF A NUMBER:**

Whenever a number is given to take square root there is 2 steps involved

Step 1:Is to check whether the given number is perfect square number or not

Step 2:Finding Square Root of given number

**STEP 1:**

There is 3 condidtion,

**Condition 1:**

The given number should not end with 2,3,7,8….

Example:

523,628 These numbers end with 2 & 8 therefore this is not a perfect square number.

**Condition 2:**

The sum of digits of a given number should be 1,4,7,9

625=6+2+5=13=1+3=4

Therefore the number is perfect square number

**Condition 3:**

The number should be prime factor which should have powers as 2,4

Example:

1)250

Here the Powers of prime factor are not 2 & 4,therefore this number is not a Perfect Square number.If you become well verse in finding the square root of a number then you will say whether the number is perfect square number or not by just looking into the number itself.

Given number should satisfy all the above mentioned 3 conditions to be a perfect square number.

**1)Find the Square root of 4761.**

**STEP 1:**

**TO CHECK WHETHER THE GIVEN NUMBER IS PERFECT SQUARE NUMBER OR NOT:**

**Condition 1:**

The number should not end with 2,3,7 & 8

Our number ends with 1 So,It satisfies 1st condition.

**Condition 2:**

The sum of digits of a given number should be 1,4,7 & 9

My Number is 4761=4+7+6+1=18=1+8=**9**

**Condition 3:**

The Power of Prime Factor may 2,4

**4761**

It’s Satisfies the above **three Condition**

**STEP 2:**

### FINDING UNIT DIGIT:

Take Unit Digit of any given number ends with 1,4,5,6,9,0…

**Note:**

1)If given number ends with **1** then the unit digit of number may be **1,9**

2)If given number ends with **4** then the unit digit of a number may be **2,8**

3)If given number ends with **5** then the unit digit of a number may be **5**

4)If given number ends with **6** then the unit digit of a number may be **4,6**

5)If given number ends with **9** then the unit digit of a number may be **3,7**

6)If given number ends with **0** then the unit digit of a number may be **0**

In our Example:

476**1**

The Last number ends with **1,**So the unit digit of the number may be **1** or **9**

**STEP 3:**

### FINDING TEN’S DIGIT:

Since we are going to find square root of a number,Leave the last 2 digits of the given number and take the remaining number & Check which is nearest perfect square number

In our Example:

**47**61

Leave the last two digit,then Remaining number is 47

Nearest Perfect Square number to 47 is **36 **which is perfect square of **6**

So,the number may be Either **61** or **69**

**STEP 4:**

**FINDING EXACT SQUARE ROOT:**

Now to identify which number is Perfect square,

√4761=**69**

### Now Let us **Find the Square Root of the Imperfect Square number.**

**Example:√128**

**STEP 1:**

Whenever the number is given,Consider the nearest Perfect Square number

Eg:128 Nearest Perfect Square =121=**11²**

**STEP 2:**

1)Subtract the given number with the Perfect Square =128 -121=**7**

2)Then the format for writing the Square Root of a number

=Nearest Square (Difference / 2* Nearest Square )

=11 (7/2*11)

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