@The-Blade-Dancer Thank you for asking and thanks for being curious. The reason choice i.) is incorrect is because in general, for any numbers \(a\) and \(b,\) the following isn't true: $$ \sqrt{ a + b } = \sqrt{a} + \sqrt{b} $$ You could try some values of \(a\) and \(b\) to see this. Like for example, \(a = 1\) and \(b = 4.\) Then let's check our statement. $$ \sqrt{ 1 + 4 } \stackrel{?}{=} \sqrt{1} + \sqrt{4} $$ $$ \sqrt{ 5} \stackrel{?}{=} 1 + 2 $$ $$ \sqrt{5} \neq 3 $$ The answer choice i.) is claiming that the following is true: $$ \sqrt{ 6 + 5\sqrt{2}} = \sqrt{6} + \sqrt{5\sqrt{2}} $$ However, this is just the same as the statement \(\sqrt{a + b} = \sqrt{a} + \sqrt{b} \) where \(a = 6\) and \(b = 5\sqrt{2}.\) And since we just showed that this statement is false, then choice i.) can't be true.