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JAMB 1990 · UME · Q9

Simplify 27+33\sqrt{27} + \dfrac{3}{\sqrt3}.

Worked solution (try it first)
  1. Take out the square factor: 27=9×3\sqrt{27} = \sqrt9 \times \sqrt3, which is 333\sqrt3.
  2. Rationalise the second term: 33=333\dfrac{3}{\sqrt3} = \dfrac{3\sqrt3}{3}, which is 3\sqrt3.
  3. Add the like surds: 33+3=433\sqrt3 + \sqrt3 = 4\sqrt3, option A.

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