MathsFreePrintable

Powers and Roots

A free, printable maths worksheet ready for your classroom. Download instantly, print, and hand out to your students — no account needed.

Powers and Roots worksheet preview

Powers and Roots

📚 Part 1: Understanding Exponents

1. Write each repeated multiplication using exponents:

a) 4 × 4 × 4 = _______

b) 7 × 7 = _______

c) 2 × 2 × 2 × 2 × 2 = _______

d) 9 × 9 × 9 = _______

2. Calculate the following powers:

a) 3² = _______

b) 5³ = _______

c) 6² = _______

d) 2⁴ = _______

3. Multiple choice: What does the base represent in the expression 4³?

The number being multiplied repeatedly

How many times to multiply

The final answer

The operation being performed

4. Show your working to calculate 8²:

🔢 Part 2: Square Numbers and Square Roots

5. Fill in the missing square numbers up to 100:

1² = 1, 2² = 4, 3² = 9, 4² = _____, 5² = _____, 6² = _____, 7² = _____, 8² = _____, 9² = _____, 10² = _____

6. Find the square roots:

a) √25 = _______

b) √49 = _______

c) √81 = _______

d) √100 = _______

7. Multiple choice: Which statement about square roots is correct?

Square roots are always positive numbers

Square roots are the inverse operation of squaring

All numbers have square roots

Square roots are always whole numbers

8. Check all the perfect square numbers:

16

20

36

50

64

🧠 Part 3: Problem Solving

9. A square garden has an area of 64 square metres. What is the length of each side?
10. Estimate whether √50 is closer to 7 or 8. Explain your reasoning:
11. Pattern investigation: Look at these calculations and describe the pattern you notice:

1² = 1

11² = 121

111² = 12321

What do you think 1111² equals? Explain your reasoning:

12. Challenge: If 2⁴ = 16, use this information to find √16 without calculating 2⁴ first. Explain your method:

About This Worksheet

Free Download

No sign-up, no email, no paywall. Just download and print.

Print-Ready

Formatted for standard paper. Clean layout, easy to read.

AI-Generated

Created with Kuraplan's AI, designed for real classroom use.

For Teachers & Parents

Use in classrooms, for homework, tutoring, or homeschool.

Need a custom version of this worksheet?

Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.

Generate Custom Worksheets — Free
No credit card Curriculum-aligned Under 60 seconds