Surds

Question

Simplify \(\sqrt{125x^{3}}\)

Solution

Show solution Hide solution Fully worked — 2 steps

1. 1
   Split into a perfect-square factor and a remaining surd

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

   \[ \sqrt{125x^{3}} = \left(\sqrt{(25x^{2})} \times \sqrt{(5x)}\right) \]
2. Final answer

   Evaluating \(\sqrt{25x^{2}} = 5x\):

   \[ \sqrt{125x^{3}} = 5x\sqrt{5x} \]

   That is, the simplified surd is five \(x\) times the square root of five \(x\).