Which of the following statements is/are true?
1. \(\sqrt {11}\) + \(\sqrt {7}\) < \(\sqrt {10}\) + \(\sqrt {8}\)
2. \(\sqrt {17}\) + \(\sqrt {11}\) > \(\sqrt {15}\) + \(\sqrt {13}\)
Answer & explanation
Correct answer: option 1
1. \(\sqrt {11}\) + \(\sqrt {7}\) < \(\sqrt {10}\) + \(\sqrt {8}\)
⇒ 11 × 7 < 10 × 8
⇒ 77 < 80 ⇒ True
2. \(\sqrt {17}\) + \(\sqrt {11}\) > \(\sqrt {15}\) + \(\sqrt {13}\)
⇒ 17 × 11 > 15 × 13
⇒ 187 > 195 ⇒ Wrong