Surds

Question

Simplify \(\sqrt{3}\left(3 + \sqrt{2}\right)\)

Solution

Show solution Hide solution Fully worked — 2 steps

1. 1
   Expand the bracket

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

   \[ \sqrt{3}\left(3 + \sqrt{2}\right) = 3\sqrt{3} + \sqrt{3 \times 2} \]
2. Final answer

   \[ \sqrt{3}\left(3 + \sqrt{2}\right) = 3\sqrt{3} + \sqrt{6} \]

   That is, the simplified expression is three times the square root of three, plus the square root of six.