Smallest integer whose square is between 15 and 30

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.

Discover how to find the smallest integer whose square falls between 15 and 30 using inequalities and square roots. This problem involves identifying the range for the square, finding square roots, and verifying the solution. Suitable for students in Grades 7-9.

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