UPCAT Mathematics practice question 18: Simplify: √72
Correct answer
B. 6√2
72 = 36 × 2, so √72 = √36 · √2 = 6√2. The form 2√18 is equal in value but not fully simplified, since 18 still contains the square factor 9.
The question
Simplify: √72
- Option A: 8√3
- Option B: 6√2Correct
- Option C: 2√18
- Option D: 36√2
Why B is correct
72 = 36 × 2, so √72 = √36 · √2 = 6√2. The form 2√18 is equal in value but not fully simplified, since 18 still contains the square factor 9.
Why the other options are wrong
- A 8√3
- Factors 72 as 24 × 3 and then mishandles the square root of 24.
- C 2√18
- Equal in value but not fully simplified, because 18 still contains the square factor 9.
- D 36√2
- Takes 36 out from under the radical without square-rooting it first.