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I have the same question as person above me (ak). Can someone please explain?

I believe \sqrt{3} x \sqrt{3} = 3 so I don't understand why the same wouldn't apply to this example.

Yes, \(\sqrt{3} * \sqrt{3} = 3\) but do we have the same expressions under the square roots in \(2*\sqrt{a+\sqrt{b}}*\sqrt{a-\sqrt{b}}\) ? NO. Under the first root we have \(a+\sqrt{b}\) (with + sign) and under another we have \(a-\sqrt{b}\) (with - sign).

So, one should do the way it's shown in the solution: \(2*\sqrt{a+\sqrt{b}}*\sqrt{a-\sqrt{b}}=2\sqrt{(a+\sqrt{b})(a-\sqrt{b})}=2\sqrt{a^2-b}\) (by applying \((x+y)(x-y)=x^2-y^2\)).