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Home >> Square Root >> Square Root by Repeated Subtraction Method >> Square Root by Repeated Subtraction Method
Before you understand how to calculate square root by repeated subtraction method, you are adviced to read:
What is Square Root ?
Property 4 of Square
As explained in Property 4 of Square Numbers that square number is the sum of successive odd numbers starting from 1.
Therefore, you can find square root of a number by repeatedly subtracting successive odd numbers(starting from 1) from the given square number, till you get zero.
Example 1: Find square root of 9 by repeated subtraction method.
Solution: This proceeds as:
Step 1: 9 – 1 = 8
Step 2: 8 – 3 = 5
Step 3: 5 – 5 = 0
As you can see that given number 9 was repeatedly subtracted by successive odd numbers (starting from 1) and we get zero in third step.
Therefore 3 is the square root of 9
Or we can also write it as:
√ 9 = 3
Example 2: Find square root of 16 by repeated subtraction method.
Solution: This proceeds as:
Step 1: 16 – 1 = 15
Step 2: 15 – 3 = 12
Step 3: 12 – 5 = 7
Step 4: 7 – 7 = 0
As you can see that given number 16 was repeatedly subtracted by successive odd numbers (starting from 1) and we get zero in forth step. Therefore 4 is the square root of 16
Or we can also write it as:
√ 16 = 4
Example 3: Find square root of 64 by repeated subtraction method.
Solution: This proceeds as:
Step 1: 64 – 1 = 63
Step 2: 63 – 3 = 60
Step 3: 60 – 5 = 55
Step 4: 55 – 7 = 48
Step 5: 48 – 9 = 41
Step 6: 41 – 11 = 30
Step 7: 30 – 13 = 17
Step 8: 17 – 17 = 0
As you can see that given number 64 was repeatedly subtracted by successive odd numbers (starting from 1) and we get zero in eighth step. Therefore 8 is the square root of 64
Or we can also write it as:
√ 64 = 8
Example 4: Find square root of 225 by repeated subtraction method.
Solution: This proceeds as:
Step 1: 225 – 1 = 224
Step 2: 224 – 3 = 221
Step 3: 221 – 5 = 216
Step 4: 216 – 7 = 209
Step 5: 209 – 9 = 200
Step 6: 200 – 11 = 189
Step 7: 189 – 13 = 176
Step 8: 176 – 15 = 161
Step 9: 161 – 17 = 144
Step 10: 144 – 19 = 125
Step 11: 125 – 21 = 104
Step 12: 104 – 23 = 81
Step 13: 81 – 25 = 56
Step 14: 56 – 27= 29
Step 15: 29 – 29 = 0
As you can see that given number 225 was repeatedly subtracted by successive odd numbers (starting from 1) and we get zero in fifteenth step. Therefore 15 is the square root of 225
Or we can also write it as:
√ 225 = 15


