Surds

Question

Write \(\sqrt{150}\) in the simplified form \(a\sqrt{n}\)

Solution

Show solution Hide solution Fully worked — 2 steps

1. 1
   Split \(\sqrt{150}\) into perfect-square factors

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

   \[ \sqrt{150} = \left(\sqrt{25} \times \sqrt{6}\right) \]
2. Final answer

   \[ \sqrt{150} = 5\sqrt{6} \]

   That is, in the simplified form \(a\sqrt{n}\), the square root of one hundred and fifty is five times the square root of six.