Question

find the square roots of 144 and 81 by the method of repeated subtraction​

Answer 1

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44-1=143, 143-3=140, 140-5=135, 135-7=128, 128-9=119, 119-11=108, 108-13=95, 95-15=80, 80-17=63, 63-19=44, 44-21=23, 23-23=0, √144=12.

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Answer 2

Answer:

The square roots of 144 and 81 are 12 and 9 respectively.

Step-by-step explanation:

• By the property of square numbers, we can say that if a natural number is a square number, then it has to be the sum of successive odd numbers starting from 1.
• By using this property ,we can find out the square root of a number by repeated subtraction method.
• We can find the square root of a number by repeatedly subtracting successive odd numbers from the given square number, till we get zero. 

144 - 1 = 143

143 - 3 = 140

140 - 5 = 135

135 - 7 = 128

128 - 9 = 119

119 - 11 = 108

108 - 13 = 95

95 - 15 = 80

80 - 17 = 63

63 - 19 = 44

44 - 21 = 23

23 - 23 = 0

As we can see that the last difference is zero, 144 is a perfect square.

As we have performed repeated subtraction 12 times, we can say that the square root of 144 is 12 . After the 12 the subtraction, we got the remainder zero.

Similarly,

81 - 1 = 80

80 - 3 = 77

77 - 5 = 72

72 - 7 = 65

65 - 9 = 56

56 - 11 = 45

45 - 13 = 32

32 - 15 = 17

17 - 17 = 0

Since the last difference is zero, 81 is a perfect square.

The square root of 81 is 9 as we have performed repeated subtraction 9 times. After the 9 the subtraction, we got the remainder zero.

For more examples of repeated subtraction​ method, click here ->

https://brainly.in/question/1224267

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