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NECO 2023 · Paper 1 · Q4

Simplify 2510\dfrac{2\sqrt5}{\sqrt{10}}.

Worked solution (try it first)
  1. Split the bottom: 10=5×2\sqrt{10} = \sqrt5 \times \sqrt2.
  2. Cancel 5\sqrt5: 2552=22\dfrac{2\sqrt5}{\sqrt5\sqrt2} = \dfrac{2}{\sqrt2}.
  3. Rationalise: 22=222\dfrac{2}{\sqrt2} = \dfrac{2\sqrt2}{2}, which is 2\sqrt2.
  4. So option C.

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