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,

HOW TO SQUARE & 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:

Whenever a number is given to take square root,just see whether a given number is perfect square number or not,

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:

4761

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:

4761

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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