Let's go through the odd-numbered questions from the worksheet:

Find the square of each number:

1. $3^2 = 9$
2. $10^2 = 100$

Find the cube of each number:

5. $2^3 = 8$
6. $10^3 = 1000$

Solve:

9. List the perfect squares between 25 and 100: Perfect squares: $36, 49, 64, 81$

10. Evaluate expressions and identify patterns: $a.\ 2^2 - 1^2 = 4 - 1 = 3$
    $b.\ 3^2 - 2^2 = 9 - 4 = 5$

Observations:

In part 11, the difference between the squares of consecutive integers results in odd numbers. For example:

• $2^2 - 1^2 = 3$
• $3^2 - 2^2 = 5$

This pattern holds because the difference between consecutive squares, $n^2 - (n-1)^2$, simplifies to $2n - 1$, which is always an odd number.

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Would you like a more detailed explanation or help with even-numbered problems?

Questions for Further Exploration:

1. What is the formula for finding the square of a number?
2. How do you calculate the cube of any given number?
3. Why are perfect squares important in mathematics?
4. Can you find a general formula for the difference of two consecutive squares?
5. How can the pattern in problem 11 be applied in broader contexts?

Tip:

When working with perfect squares and cubes, always check for easy-to-calculate numbers first, like 1, 4, 9, 16, etc. This can help simplify problems quickly!