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Powers and Square Roots

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Powers and Square Roots

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📚 Part 1: Powers and Square Roots

1. Calculate the following powers:

a) 3² = _____

b) 5³ = _____

c) (-2)⁴ = _____

d) -2⁴ = _____

2. Find the square roots of these perfect squares:

a) √16 = _____

b) √81 = _____

c) √144 = _____

d) √225 = _____

3. Which of these statements is correct?

(-3)² = -9

(-3)² = 9

-3² = 9

Both b and c are correct

4. A square garden has an area of 49 square metres. What is the length of one side?

✏️ Part 2: Order of Operations with Powers and Roots

5. Use GEMA (Grouping, Exponents, Multiplication/Division, Addition/Subtraction) to solve:

a) 3 + 2² × √16 = ___________

b) 5² - 3 × √9 + 2 = ___________

6. Circle the expressions that equal 36:

√1296

2³ + 4²

3² × 2²

7. Explain why (2 + 3)² ≠ 2² + 3²:

🎯 Part 3: Problem Solving

8. A square tile has an area of 64 cm². If you arrange 9 of these tiles in a 3×3 pattern, what is the total area?
9. Complete this pattern:

1² = 1

2² = 4

3² = 9

4² = ____

5² = ____

What do you notice about the differences between consecutive square numbers?

10. Challenge: If 2ⁿ = 64, what is the value of n?

n = ____

Show your reasoning:

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