Examine, whether the following number is rational or irrational:
$(3 + \sqrt{3}) + (3 - \sqrt{3})$ .

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Solution

$(3 + \sqrt{3}) + (3 - \sqrt{3})$
$= 3 + \sqrt{3} + 3 - \sqrt{3}$
$= 3 + 3 = 6$ .
Since the number $6$ is a rational number, $(3 + \sqrt{3}) + (3 - \sqrt{3})$ is a rational number.

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