Question
Simplify:
$\big(\sqrt{5}-\sqrt{2}\big)\big(\sqrt{2}-\sqrt{3}\big)$
$\big(\sqrt{5}-\sqrt{2}\big)\big(\sqrt{2}-\sqrt{3}\big)$
✓
Answer
$\big(\sqrt{5}-\sqrt{2}\big)\big(\sqrt{2}-\sqrt{3}\big)$
$=\sqrt{5}\big(\sqrt{2}-\sqrt{3}\big)-\sqrt{2}\big(\sqrt{2}-\sqrt{3}\big)$
$=\Big(\sqrt{10}-\sqrt{15}-2+\sqrt{16}\Big)$
$=\sqrt{5}\big(\sqrt{2}-\sqrt{3}\big)-\sqrt{2}\big(\sqrt{2}-\sqrt{3}\big)$
$=\Big(\sqrt{10}-\sqrt{15}-2+\sqrt{16}\Big)$
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