Square Root Using Successive Subtraction of Odd Numbers


 
 
Concept Explanation
 

Square Root Using Successive Subtraction of Odd Numbers

This method can be used for small perfect squares say up to 250. The steps to be followed are as follows

Step I: Obtain the number whose square root is to be found.

Step II: Subtract the odd numbers 1,3,5,7,9,13,15,...successively from the given number.

Step III: If the given number is a perfect square, we will get zero at some stage. We stop at the point where we have got zero.

Step IV: The number of times we have performed subtraction will be the square root of the given number.

Illustration: Find the square root of 64 by successive subtraction of odd numbers.

Solution: Subtracting the odd numbers successively, we get

64 - 1 = 63

63 - 3 =60

60 - 5 = 55

55 - 7 = 48

48 - 9 = 39

39 - 11 = 28

28 - 13 = 15

15 - 15 = 0

Hence, we performed subtraction 8 times.

therefore,large sqrt{64}=8

Illustration: Find the square root of 25 by successive subtraction of odd numbers.

Solution: Subtracting the odd numbers successively, we get

25 - 1 =24

24 - 3 =21

 21 - 5 =16

16 - 7 = 9

 9 - 9 = 0

Hence, we performed subtraction 5 times.

therefore,large sqrt{25}=5

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Sample Questions
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Question : 1

What is the number obtained in the 4th step after subtracting odd numbers while calculating the square root of 10 by the method of "successive subtraction of odd numbers" ?

Right Option : D
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Explanation
Question : 2

What is the number obtained in the 19th step after subtracting odd numbers while calculating the square root of 441 by the method of "successive subtraction of odd numbers"  ?

Right Option : A
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Explanation
Question : 3

What is the number obtained in the 5th step after subtracting odd numbers while calculating the square root of 49 by the method of "successive subtraction of odd numbers"  ?

Right Option : A
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Explanation
 
 


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