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:
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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