Question

5 which of the following square roots would not be between 7 and 8 a √50 b √62 c √45 d √53

Explanation:

Step1: Find the range of squares

We know that if \(7 < \sqrt{x}< 8\), then squaring all parts (since squaring is a monotonic increasing function for non - negative numbers), we get \(7^{2}

Step2: Check each option

• For option A: \(x = 50\). Since \(49<50<64\), so \(\sqrt{50}\) is between \(7\) and \(8\).
• For option B: \(x = 62\). Since \(49<62<64\), so \(\sqrt{62}\) is between \(7\) and \(8\).
• For option C: \(x = 45\). Since \(45<49\), so \(\sqrt{45}\) is not between \(7\) and \(8\) (because if \(x = 45\), \(\sqrt{45}<\sqrt{49} = 7\)).
• For option D: \(x = 53\). Since \(49<53<64\), so \(\sqrt{53}\) is between \(7\) and \(8\).

Answer:

C. \(\sqrt{45}\)