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Find by long division, pairing outward from the decimal point as 59 . 29

Class 8Squares and Square RootsSquares and Roots
  • A77
  • B7.7
  • C0.77
  • D29.645

Step-by-Step Solution

There is one period before the point and one after it, so the root has one digit before the point and one after. ≤ 59, remainder 10; bring down 29 to get 1029; double 7 to get 14, and exactly. The root is 7.7 . The traps 77 and 0.77 misplace the decimal point, and 29.645 halves 59.29.
Answer: B) 7.7

Key idea: Square root of decimals

Pair digits from the **decimal point outward** — that is, leftward for the integer part, rightward for the decimal part. Add zeros on the right of the decimal as needed to make full pairs.

Example: . Pair: .06 25. The integer part is empty. Apply long division on the paired form. Result: 0.25 (since ).

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