Between which two integers will √5 lie on the number line?

Correct answer: 2 and 3

To locate √5 between consecutive integers, compare 5 with nearby perfect squares. We know that 2² = 4 and 3² = 9. Since 4 < 5 < 9, taking positive square roots gives 2 < √5 < 3. Thus √5 lies between the integers 2 and 3, and option A is correct. In fact, √5 is approximately 2.236, which confirms the same placement, although the perfect-square comparison is the exact and more useful method. Option B would contain numbers whose squares range only from 1 to 4, so it cannot contain √5. Options C and D are also impossible because their intervals are respectively much larger and much smaller than the value determined by the inequalities. The governing concept is ordering irrational numbers through neighboring perfect squares.