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Using long division, find . Pair the digits from the right as 8 | 41.

Class 8Squares and Square RootsSquares and Roots
  • A29
  • B21
  • C41
  • D420.5

Step-by-Step Solution

First period is 8: the largest digit whose square is at most 8 is , remainder 4. Bring down 41 to get 441. Double the quotient 2 to get 4, then find with ≤ 441: gives exactly. Quotient = 29, and . The trap 21 stops at too small a value of , 41 just copies the second period, and 420.5 halves 841.
Answer: A) 29

Key idea: Square root by long division

Use this for larger numbers (or non-perfect squares).

**Step 1**: Pair the digits from the right (e.g. 1849 → 18 49).
**Step 2**: Find the largest integer whose square ≤ first pair. Write it as the first quotient digit. Subtract its square.
**Step 3**: Bring down the next pair. Double the current quotient — that's your divisor's prefix. Find a digit such that (prefix × ≤ current dividend.
**Step 4**: Append to quotient, subtract, repeat.

Example: ≤ 18; remainder 2; bring down 49 → 249; double 4 = 8; find where ≤ 249; gives .) Quotient = 43.

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