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Algebra

Question 15 of 20

Surds

Question

Rationalise the denominator in \(\dfrac{2\sqrt{3}}{\sqrt{13}}\)

Show solution Hide solution Fully worked — 3 steps
  1. Multiply the numerator and denominator by \(\sqrt{13}\)

    Using the rule \(\frac{b}{\sqrt{a}} = \frac{b}{\sqrt{a}} \times \frac{\sqrt{a}}{\sqrt{a}} = \frac{b\sqrt{a}}{a}\):

    \[ \frac{2\sqrt{3}}{\sqrt{13}} = \frac{2\sqrt{3}}{\sqrt{13}} \times \frac{\sqrt{13}}{\sqrt{13}} \]
  2. Multiply the surds

    Using the rule \(\sqrt{a} \times \sqrt{b} = \sqrt{(a \times b)}\):

    \[ = \frac{2\sqrt{3 \times 13}}{13} \]
  3. Final answer
    \[ \frac{2\sqrt{3}}{\sqrt{13}} = \frac{2\sqrt{39}}{13} \]

    That is, with the denominator rationalised, the answer is two times the square root of thirty-nine, over thirteen.