Page 32 - Concepts of Reasoning-8

Worksheet-3.3

Square Roots by Repeated Subtraction

1. Find and correct the errors in the following problems on finding the square roots by repeated
subtraction method :

a. Ö9 = _____
i. 9 – 1 = 8 ii. 8 – 3 = 6 iii. 6 – 5 = 1

Since the subtraction of successive odd numbers from 9 does not lead to 0, 9 is not a perfect
square.

Error :
Correction :

b. Ö121 = _____

i. 121 – 1 = 120 ii. 120 – 3 = 117 iii. 117 – 5 = 112 iv. 112 – 7 = 105 v. 105 – 9 = 96
vi. 96 – 11 = 85 vii. 86 – 13 = 73 viii. 73 – 15 = 58 ix. 58 – 17 = 41 x. 41 – 19 = 22

xi. 22 – 21 = 1
Since the subtraction of successive odd numbers from 121 does not lead to 0, 121 is not a
perfect square.

Error :
Correction :

c. Ö26 = _____
i. 26 – 1 = 25 ii. 25 – 3 = 22 iii. 22 – 5 = 16 iv. 16 – 7 = 9 v. 9 – 9 = 0
Since the subtraction of successive odd number from 26 lead to 0 in the 5th step, the square-
root of 26 is 5.

Error :
Correction :

32 Reasoning - 8