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Algebra

Question 7 of 20

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Question

Simplify \(\dfrac{\sqrt{147}}{4} \div \dfrac{\sqrt{27}}{2}\)

Show solution Hide solution Fully worked — 4 steps
  1. Split 147 and 27 into perfect-square factors

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

    \[ \frac{\sqrt{147}}{4} \div \frac{\sqrt{27}}{2} = \frac{\left(\sqrt{49} \times \sqrt{3}\right)}{4} \div \frac{\left(\sqrt{9} \times \sqrt{3}\right)}{2} \]
  2. Evaluate \(\sqrt{49}\) and \(\sqrt{9}\)
    \[ = \frac{7\sqrt{3}}{4} \div \frac{3\sqrt{3}}{2} \]
  3. Divide the fractions

    Since \(\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}\):

    \[ = \frac{14\sqrt{3}}{12\sqrt{3}} \]
  4. Final answer

    Cancelling \(\sqrt{3}\) and simplifying \(\frac{14}{12}\):

    \[ \frac{\sqrt{147}}{4} \div \frac{\sqrt{27}}{2} = \frac{7}{6} \]

    That is, the result is seven sixths.