<s>[INST] Multiplying square roots How do I simplify the following types of question:
$ \sqrt{x^2+5} \times \sqrt{x^2+20}$
Do I need to get both answer out of their roots first or not? This is how I would do it:
$ \sqrt{x^2+5} \times \sqrt{x^2+20} =  x^2 + x\sqrt{20} + x\sqrt{5} + \sqrt{100}$ but I'm very certain this isn't the correct way.
 [/INST] For positive real $a,b,c,d$
$\sqrt{a+b}\cdot\sqrt{c+d}=\sqrt{(a+b)(c+d)}=\sqrt{ac+ad+bc+bd}$ which is $\ne \sqrt{ac}+\sqrt{ad}+\sqrt{bc}+\sqrt{bd}$
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