The two shorter sides of a right-angled triangle measure 9 cm and 40 cm. How long is the hypotenuse?
Class 8Squares and Square RootsSquares and Roots
A49 cm
B41 cm
C31 cm
D1681 cm
Step-by-Step Solution
Hypotenuse2=92+402=81+1600=1681, so the hypotenuse is 1681=41 cm (9, 40, 41 is a Pythagorean triplet). The trap 49 comes from simply adding 9 + 40, and 31 from subtracting them. The trap 1681 stops at the square and forgets the final square root.
Answer: B) 41 cm
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 d such that (prefix × 10+d)×d ≤ current dividend. **Step 4**: Append d to quotient, subtract, repeat.
Example: 1849=43.(42=16 ≤ 18; remainder 2; bring down 49 → 249; double 4 = 8; find d where (80+d)d ≤ 249; d=3 gives 83×3=249.) Quotient = 43.
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