<s>[INST] Simplify $\sqrt{10 + \sqrt{24} + \sqrt{40} + \sqrt{60}} $ Simplify
$$ \sqrt{10 + \sqrt{24} + \sqrt{40} + \sqrt{60}} $$

Attempt:
$$ \sqrt{10 + \sqrt{24} + \sqrt{40} + \sqrt{60}}  =  \sqrt{10 + 2\sqrt{6} + 2\sqrt{10} + 2\sqrt{15}} = \sqrt{10 + 2(\sqrt{6} + \sqrt{10} + \sqrt{15})} $$
let $X =\sqrt{10 + \sqrt{24} + \sqrt{40} + \sqrt{60}}$, then
$$ X^{2} = 10 + 2(\sqrt{6} + \sqrt{10} + \sqrt{15}) $$
How to continue?
 [/INST] You can continue so:
$$x^2=10 + 2(\sqrt{6} + \sqrt{10} + \sqrt{15})=2+5+3+ 2(\sqrt{6} + \sqrt{10} + \sqrt{15})=(\sqrt2+\sqrt5+\sqrt3)^2.$$
Can you end it now?
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