To find the smallest integer whose square is between 15 and 30, we can proceed as follows:

1. Identify the range for the square: $15 < n^2 < 30$.

2. Determine the smallest integer $n$ that satisfies this inequality.

Start by finding the square roots of 15 and 30: $\sqrt{15} \approx 3.87$ $\sqrt{30} \approx 5.48$

The smallest integer greater than 3.87 is 4. Let's check if $n = 4$ satisfies the inequality: $4^2 = 16$

Since $16$ is within the range $15 < n^2 < 30$, the smallest integer $n$ whose square is between 15 and 30 is $n = 4$.

Would you like more details or have any questions? Here are some additional questions you might find interesting:

1. What is the largest integer whose square is less than 100?
2. How do you find the square root of a number manually?
3. What is the smallest integer whose cube is greater than 100?
4. How can you approximate square roots without a calculator?
5. What is the difference between rational and irrational numbers?

Tip: When solving inequalities involving squares, it's helpful to consider the square roots of the boundary values to narrow down the possible integers.