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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

  1. Option A: 8√3
  2. Option B: 6√2Correct
  3. Option C: 2√18
  4. 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.

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