Identify the incorrect relationship(s) from the list below: (i) \(\sqrt{6} + \sqrt{2} = \sqrt{5} + \sqrt{3}\) (ii) \(\sqrt{6} + \sqrt{2} < \sqrt{5} + \sqrt{3}\) (iii) \(\sqrt{6} + \sqrt{2} > \sqrt{5} + \sqrt{3}\)
(i) and (iii)
Compute: \(\sqrt{6} \approx 2.449,\ \sqrt{2} \approx 1.414 \Rightarrow \sqrt{6}+\sqrt{2} \approx 3.863\)
\(\sqrt{5} \approx 2.236,\ \sqrt{3} \approx 1.732 \Rightarrow \sqrt{5}+\sqrt{3} \approx 3.968\)
Therefore \(\sqrt{6}+\sqrt{2} < \sqrt{5}+\sqrt{3}\) — statement (ii) is correct.
Statements (i) (equality) and (iii) (greater than) are both incorrect.
Hence the answer is (i) and (iii).
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