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Algebra

Question 14 of 20

Surds

Question

Rationalise the denominator in \(\dfrac{60}{\sqrt{15}}\)

Show solution Hide solution Fully worked — 3 steps
  1. Multiply the numerator and denominator by \(\sqrt{15}\)

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

    \[ \frac{60}{\sqrt{15}} = \frac{60}{\sqrt{15}} \times \frac{\sqrt{15}}{\sqrt{15}} \]
  2. Multiply the fractions
    \[ = \frac{60\sqrt{15}}{15} \]
  3. Final answer

    Simplifying \(\frac{60}{15}\):

    \[ \frac{60}{\sqrt{15}} = 4\sqrt{15} \]

    That is, with the denominator rationalised, the answer is four times the square root of fifteen.