JAMB 2011 · UTME · Q9

Simplify $\left(\sqrt2 + \dfrac{1}{\sqrt3}\right)\left(\sqrt2 - \dfrac{1}{\sqrt3}\right)$ .

Worked solution (try it first)

The brackets are $(a + b)(a - b)$ , a difference of two squares: $a^2 - b^2$ .
Here $a^2 = (\sqrt2)^2 = 2$ and $b^2 = \left(\frac{1}{\sqrt3}\right)^2$
$= \frac13$ .
So the value is $2 - \frac13 = \frac53$ , option B.