Which value lies between ( \sqrt{2.25} ) and ( \sqrt{2.56} ) on the number line?

Correct answer: (1.55)

The direct answer is option B: 1.55. First evaluate the two square roots: \(\sqrt{2.25}=1.5\), because \(1.5^2=2.25\); and \(\sqrt{2.56}=1.6\), because \(1.6^2=2.56\). Thus the question asks for a value strictly between 1.5 and 1.6. Now check the options: 1.4 is below 1.5, 1.55 is between 1.5 and 1.6, 1.7 is above 1.6, and 1.2 is below 1.5. Therefore option B is correct. Option A is too small, option C is too large, and option D is also too small. The decimal points do not change the method: find the positive square roots and compare ordinary decimal values. Memory cue: square the endpoints mentally; \(1.5^2=2.25\) and \(1.6^2=2.56\), so any answer between 1.5 and 1.6 works, and only 1.55 is offered.