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Question
Find the square root of: 27.3529
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Solution
27.3529
| 5.23 | |
| 5 | 27.3529 25 |
| 102 | 2.35 2.04 |
| 1043 | 3129 3129 |
| x |
Required square root = 5.23
Notes
Step-by-step Breakdown
1. Find the square root of 27 (first pair)
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Closest square less than 27: 52=255^2 = 2552=25
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So, write 5 as the first digit of the square root.
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Subtract: 27−25=227 - 25 = 227−25=2
Now bring down next pair → 35
Now we have: 235235235
2. Double the current quotient (5) → 10
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Write 102 | 2.35 (that "102" comes from 10 + _; we are finding that _ digit)
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Try: 102 × 2 = 204
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Subtract: 235−204=31235 - 204 = 31235−204=31
Bring down next pair: 29
Now we have: 3129
3. Current root is 5.2, double it: 10.4
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Use it to find the next digit:
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Try: 1043 × 3 = 3129
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Perfect match!
-
-
Subtract: 3129−3129=03129 - 3129 = 03129−3129=0
Now there’s nothing left — remainder is 0.
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