\(\sqrt{\frac{0.204\times42}{0.07\times3.4}}\) is equal to
2023
\(\sqrt{\frac{0.204\times42}{0.07\times3.4}}\) is equal to
Answer: C. 6 — ConceptFor a non-negative number, the principal square root is the unique non-negative value whose square equals that number. Evaluate the expression inside…
- A.
0·06
- B.
0·6
- C.
6
- D.
More than one of the above
- E.
None of the above
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
For a non-negative number, the principal square root is the unique non-negative value whose square equals that number.
Evaluate the expression inside the radical first; decimal products and division follow the ordinary place-value rules.
Application
Compute the numerator: 0.204 × 42 = 8.568.
Compute the denominator: 0.07 × 3.4 = 0.238.
Divide inside the radical: 8.568 ÷ 0.238 = 36.
Take the principal square root: √36 = 6.
Cross-check
Squaring 6 gives 62 = 36, which matches the value obtained inside the radical. Therefore, the expression equals 6.