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).
Similar Questions
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Important Questions from Rational or Irrational Numbers
Which of the following number is irrational?
Which of the following numbers will have an irrational square root?
What is the square root of 16 + 6√7?
A non-terminating but recurring decimal is:
Which of the following is false?
