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 the property of square - roots

If \(a^2 < n < b^2\), then \(a<\sqrt{n}0\).

Step2: Check option A

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

Step3: Check option B

Since \(5^2 = 25\) and \(6^2 = 36\), and \(25<36\), but \(37>36\), so \(\sqrt{37}>6\), the statement \(5 < \sqrt{37}<6\) is incorrect.

Step4: Check option C

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

Step5: Check option D

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

Answer:

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