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Algebra

Question 2 of 20

Surds

Question

Simplify \(\dfrac{10\sqrt{3}}{\sqrt{5}}\)

Show solution Hide solution Fully worked — 3 steps
  1. Multiply the numerator and denominator by \(\sqrt{5}\)

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

    \[ \frac{10\sqrt{3}}{\sqrt{5}} = \frac{10\sqrt{3}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} \]
  2. Multiply the surds

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

    \[ = \frac{10\left(\sqrt{15}\right)}{5} \]
  3. Final answer

    Since \(\frac{10}{5} = 2\):

    \[ \frac{10\sqrt{3}}{\sqrt{5}} = 2\sqrt{15} \]

    That is, the simplified surd is two times the square root of fifteen.