Let's carefully examine why $-5$ cannot be the smallest integer whose square lies between 15 and 30.

1. Check the square of $-5$: $(-5)^2 = 25$ Since $25$ is indeed between 15 and 30, $-5$ satisfies the condition for the square value.

2. Check the requirement for "smallest integer":

   • The term "smallest integer" typically refers to the integer with the smallest absolute value (the closest to zero) that meets the condition.

3. Considering negative values:

   • Even though $-5$ satisfies the condition for the square value, the smallest integer (considering absolute value and closeness to zero) whose square falls within the given range is $4$.

So, while $-5$ satisfies the square condition, the smallest positive integer whose square is between 15 and 30 is $4$, because $4$ is closer to zero than $-5$.

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 determining the "smallest" or "largest" integer for mathematical problems, always consider the absolute value and the proximity to zero unless specifically asked for negative values.