Perfect Squares and Cubes Practice Problems with Solutions

📚 Topic Summary

Perfect squares are numbers that result from squaring an integer (multiplying it by itself). For instance, 9 is a perfect square because it's $3 \times 3 = 3^2$. Perfect cubes, on the other hand, are numbers that result from cubing an integer (multiplying it by itself twice). For example, 8 is a perfect cube because it's $2 \times 2 \times 2 = 2^3$. Understanding these concepts is crucial for simplifying radicals and solving algebraic equations.

This worksheet will test your knowledge of perfect squares and cubes, helping you to identify them and understand their properties through a mix of vocabulary, fill-in-the-blanks, and critical thinking questions. Let's get started!

🧠 Part A: Vocabulary

Match each term with its correct definition:

1. 1-c
2. 2-a
3. 3-b
4. 4-d
5. 5-e

✍️ Part B: Fill in the Blanks

Complete the following paragraph with the correct terms:

A _______ is a number that can be obtained by squaring an integer. For example, 25 is a perfect square because $5 \times 5 = 25$. Similarly, a _______ is a number that can be obtained by cubing an integer. For instance, 64 is a perfect cube because $4 \times 4 \times 4 = 64$. The _______ of a number is the value that, when multiplied by itself, gives the original number, while the _______ of a number is the value that, when multiplied by itself twice, gives the original number. Numbers like -3, 0, and 7 are examples of _______.

Answer Key: perfect square, perfect cube, square root, cube root, integers

🤔 Part C: Critical Thinking

Explain why understanding perfect squares and cubes is important in simplifying radical expressions.