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Question

Simplify each of the following expressions:
$$(\sqrt5 - \sqrt2)(\sqrt5 + \sqrt2)$$

Solution
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$$(\sqrt5 - \sqrt2)(\sqrt5 + \sqrt2)$$
$$(a + b) (a - b) = a^2 - b^2$$
$$\therefore \ \ (\sqrt5 - \sqrt2)(\sqrt5 + \sqrt2) = (\sqrt5)^2 - (\sqrt2)^2$$
$$= 5 - 2$$
$$= 3$$

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