Standard High contrast

Algebra

Question 3 of 20

Surds

Question

Simplify \(3\sqrt{2x} - 5\sqrt{8x} + \sqrt{72x}\)

Show solution Hide solution Fully worked — 4 steps
  1. Split \(\sqrt{8x}\) and \(\sqrt{72x}\) into perfect-square factors

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

    \[ 3\sqrt{2x} - 5\sqrt{8x} + \sqrt{72x} = 3\sqrt{2x} - 5\left(\sqrt{4} \times \sqrt{2x}\right) + \left(\sqrt{36} \times \sqrt{2x}\right) \]
  2. Evaluate \(\sqrt{4}\) and \(\sqrt{36}\)
    \[ = 3\sqrt{2x} - 10\sqrt{2x} + 6\sqrt{2x} \]
  3. Collect the like surds

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

    \[ = (3 - 10 + 6)\sqrt{2x} \]
  4. Final answer
    \[ 3\sqrt{2x} - 5\sqrt{8x} + \sqrt{72x} = -\sqrt{2x} \]

    That is, the simplified expression is minus the square root of two \(x\).