Question
An irrational number between \(2\) and \(2.5\) is:
(a) \( \sqrt{11} \)
(b) \( \sqrt{5} \)
(c) \( \sqrt{22.5} \)
(d) \( \sqrt{12.5} \)
Solution
Square the interval:
\[ 2^2 = 4, \quad (2.5)^2 = 6.25 \]
So we need a number whose square lies between 4 and 6.25.
Option (a): \( \sqrt{11} \)
\(11 > 6.25\) → Not in range
Option (b): \( \sqrt{5} \)
\(5\) lies between \(4\) and \(6.25\)
✔ Correct
Option (c): \( \sqrt{22.5} \)
Too large
Option (d): \( \sqrt{12.5} \)
Too large
Final Answer
✔ Correct option: (b) \( \sqrt{5} \)