On the number line, (3+√2) lies between which two integers?

Correct answer: 4 और 5

The governing concept is bounding an irrational expression between consecutive integers. Because 1² < 2 < 2², taking positive square roots gives 1 < √2 < 2. Adding 3 to every part preserves the order, so 4 < 3 + √2 < 5. Thus the expression lies strictly between 4 and 5, making option A correct. A decimal check gives √2 ≈ 1.414 and therefore 3+√2 ≈ 4.414, which confirms the interval. Option B is incorrect because the value is greater than 4. Option C is incorrect because the value is less than 5, and option D places it even farther below the actual value. The exact inequality is sufficient; decimal approximation is only a confirmation.