JAMB 2004 · UME · Q7

Surds

Simplify $\dfrac{1}{\sqrt3 + 2}$ in the form $a + b\sqrt3$ .

Worked solution (try it first)

Multiply the top and bottom by the conjugate of the bottom, $2 - \sqrt3$ .
Bottom: $(2 + \sqrt3)(2 - \sqrt3) = 4 - 3$ , which is 1.
So the value is $2 - \sqrt3$ , option C.

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