How to rationalize this root form? Suppose that we have a equation like this: $$\sqrt{a+b+2\sqrt{ab}}$$ or $$\sqrt{a+b-2\sqrt{ab}}$$ In order to rationalize it, we can apply the formula: $$\sqrt{a} + \sqrt{b} = \sqrt{a+b+2\sqrt{ab}}$$ or $$\sqrt{a} - \sqrt{b} = \sqrt{a+b -2\sqrt{ab}}$$, where $a>b$ My question is: Is it possible to rationalize the form like this: $$\sqrt{10+2(\sqrt{15}+\sqrt{10}+\sqrt{6})}$$ ? Thanks

Notice that there are $3$ terms with $2$ so probably it will be of form $(a+b+c)^2$ $$(a+b+c)^2=a^2+b^2+c^2+2(ab+ac+bc)\\\a^2+b^2+c^2=10\\\ab=\sqrt{15}\\\ac=\sqrt{10}\\\bc=\sqrt{6}\\\b^2+c^2=10-a^2\\\a^2b^2+a^2c^2=25\\\a^2(b^2+c^2)=25\\\a^2(10-a^2)=25\\\10a^2-a^4-25=0\\\a^4-10a^2+25=0\\\\(a^2-5)^2=0\\\a=\sqrt{5}\\\ab=\sqrt{15}\implies b=\sqrt{3}\\\bc=\sqrt{6}\implies c=\sqrt{2}$$ So the answer is $\sqrt{2}+\sqrt{3}+\sqrt{5}$