Question

1. which of the following statements is incorrect? a. 1<√2<2 b. 5<√37<6 c. 9<√90<10 d. 14<√210<15

Explanation:

Step1: Recall square - number property

If \(a^2 < n<(a + 1)^2\), then \(a<\sqrt{n}

Step2: Analyze option A

Since \(1^2=1\) and \(2^2 = 4\), and \(1<2<4\), so \(1<\sqrt{2}<2\). This statement is correct.

Step3: Analyze option B

Since \(5^2=25\) and \(6^2 = 36\), and \(37>36\), so \(\sqrt{37}>6\), not \(5<\sqrt{37}<6\). This statement is incorrect.

Step4: Analyze option C

Since \(9^2=81\) and \(10^2 = 100\), and \(81<90<100\), so \(9<\sqrt{90}<10\). This statement is correct.

Step5: Analyze option D

Since \(14^2=196\) and \(15^2 = 225\), and \(196<210<225\), so \(14<\sqrt{210}<15\). This statement is correct.

Answer:

B. \(5 < \sqrt{37}<6\)