Find the square root of (0.127 × 0.13)/(1.27 × 2.197).
2026
Find the square root of (0.127 × 0.13)/(1.27 × 2.197).
Answer: D. 1/13 — ConceptTo simplify a product inside a square root, reduce convenient numerator–denominator pairs before multiplying. For a positive perfect-square fraction,…
- A.
3/13
- B.
2/13
- C.
4/13
- D.
1/13
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Correct answer: D
Concept
To simplify a product inside a square root, reduce convenient numerator–denominator pairs before multiplying.
For a positive perfect-square fraction, √(a2/b2) = a/b.
Application
Pair 0.127 with 1.27: 0.127/1.27 = 1/10.
Write 0.13 = 13/100 and 2.197 = 2197/1000 = 133/1000. Thus 0.13/2.197 = (13/100) × (1000/2197) = 10/169.
The radicand is (1/10) × (10/169) = 1/169.
Therefore √(1/169) = 1/13.
Cross-check
Squaring 1/13 gives 1/169, which equals the simplified radicand.
The square root is 1/13.