Solved Examples of Perfect Squares and Cubes: A Grade 8 Tutorial

📚 Quick Study Guide

• 🔢 A perfect square is a number that can be obtained by squaring an integer (multiplying an integer by itself). For example, 9 is a perfect square because $3 \times 3 = 9$.
• ➗ To check if a number is a perfect square, find its square root. If the square root is an integer, then the number is a perfect square.
• 🧊 A perfect cube is a number that can be obtained by cubing an integer (multiplying an integer by itself twice). For example, 8 is a perfect cube because $2 \times 2 \times 2 = 8$.
• ✨ To check if a number is a perfect cube, find its cube root. If the cube root is an integer, then the number is a perfect cube.
• ➕ Remember that 1 is both a perfect square ($1 \times 1 = 1$) and a perfect cube ($1 \times 1 \times 1 = 1$).

Practice Quiz

1. Which of the following numbers is a perfect square?
   1. 10
   2. 15
   3. 16
   4. 20
2. Which of the following numbers is a perfect cube?
   1. 9
   2. 25
   3. 27
   4. 30
3. What is the square root of 49?
   1. 5
   2. 6
   3. 7
   4. 8
4. What is the cube root of 64?
   1. 2
   2. 3
   3. 4
   4. 5
5. Which of the following is both a perfect square and a perfect cube?
   1. 4
   2. 8
   3. 9
   4. 64
6. What is the value of $5^2$?
   1. 10
   2. 15
   3. 20
   4. 25
7. What is the value of $3^3$?
   1. 9
   2. 18
   3. 27
   4. 36