Which of the following statement(s) is/are TRUE? I. \(\sqrt{1}+ \sqrt{2} + \sqrt{3} + \sqrt{4}+ \sqrt{5} + \sqrt{6} > 10\) II. \(\sqrt{(10)} + \sqrt{(12)} + \sqrt{(14)} > 3 \sqrt{(12)}\)

Which of the following statement(s) is/are TRUE? I. \(\sqrt{1}+ \sqrt{2} + \sqrt{3} + \sqrt{4}+ \sqrt{5} + \sqrt{6} > 10\) II. \(\sqrt{(10)} + \sqrt{(12)} + \sqrt{(14)} > 3 \sqrt{(12)}\) Correct Answer Only I

Statement I:

√1 + √2 + √3 + √4 + √5 + √6 > 10

Taking LHS –

⇒ LHS = 1 + 1.4 + 1.7 + 2 + 2.25 + 2.5

⇒ LHS = 10.85 which is greater than 10.

∴ It is correct.

Statement II:

√10 + √12 + √14 > 3√12

Taking LHS and calculate square root –

⇒ + +

⇒ (3.17 + 3.5 + 3.83)

⇒ 10.50

And RHS = 3√12 = 3 × (3.5) = 10.50

∴ LHS = RHS

But in the question LHS is greater than RHS which is incorrect.

∴ Only Statement I is correct answer.