Free Grade 3 Square Roots Lessons
Free Grade 3 lessons for Square Roots: 12 real questions with a full answer key and worked solutions. A power tells you how many times to multiply a number by itself. A square root undoes squaring. When multiplying powers of the same base, add the indices.
Free
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain square roots
Explain square roots accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate square roots
Calculate square roots accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare square roots
Compare square roots accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify square roots
Justify square roots accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Square Roots works
A power tells you how many times to multiply a number by itself. A square root undoes squaring. When multiplying powers of the same base, add the indices.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Work out 3² and √9.[1]
- 2.Work out 10² and √100.[1]
- 3.Work out 11² and √121.[1]
- 4.Work out 4² and √16.[1]
- 5.Evaluate 4^3.[2]
- 6.Evaluate 5^3.[2]
- 7.Evaluate 2^4.[2]
- 8.Evaluate 2^3.[2]
- 9.Simplify x^4 × x^3 ÷ x^5.[3]
- 10.Simplify x^2 × x^3 ÷ x^5.[3]
- 11.Simplify x^2 × x^3 ÷ x^3.[3]
- 12.Simplify x^2 × x^3 ÷ x^6.[3]
Show answers and working
1. 9 and 3
3² = 3 × 3 = 9 √9 = 3 because 3 × 3 = 9
2. 100 and 10
10² = 10 × 10 = 100 √100 = 10 because 10 × 10 = 100
3. 121 and 11
11² = 11 × 11 = 121 √121 = 11 because 11 × 11 = 121
4. 16 and 4
4² = 4 × 4 = 16 √16 = 4 because 4 × 4 = 16
5. 64
Multiply 4 by itself 3 times. 4 × 4 × 4 = 64
6. 125
Multiply 5 by itself 3 times. 5 × 5 × 5 = 125
7. 16
Multiply 2 by itself 4 times. 2 × 2 × 2 × 2 = 16
8. 8
Multiply 2 by itself 3 times. 2 × 2 × 2 = 8
9. x^2
Multiplying: add the powers → x^7. Dividing: subtract the powers → x^7 ÷ x^5 = x^2.
10. x^0
Multiplying: add the powers → x^5. Dividing: subtract the powers → x^5 ÷ x^5 = x^0.
11. x^2
Multiplying: add the powers → x^5. Dividing: subtract the powers → x^5 ÷ x^3 = x^2.
12. x^-1
Multiplying: add the powers → x^5. Dividing: subtract the powers → x^5 ÷ x^6 = x^-1.
Worked examples
Work out 9² and √81.
- 9² = 9 × 9 = 81
- √81 = 9 because 9 × 9 = 81
- Answer: 81 and 9
Evaluate 5^4.
- Multiply 5 by itself 4 times.
- 5 × 5 × 5 × 5 = 625
- Answer: 625
Simplify x^3 × x^5 ÷ x^3.
- Multiplying: add the powers → x^8.
- Dividing: subtract the powers → x^8 ÷ x^3 = x^5.
- Answer: x^5
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Works out 3² as 6.
Correction: 3² means 3 × 3, not 3 × 2.
Multiplies indices when multiplying powers.
Correction: x³ × x⁴ = x⁷ — add, don't multiply.
Teacher tips
- · Write powers out in full before using index laws.
Parent tips
- · Spot square numbers on tiles or a chessboard.
Real-life applications
- · Area in square units, computer storage (powers of 2).
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Square Roots
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Square Roots lesson really free?
- Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Cubes, Squares, Factors and Multiples. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Square Roots?
- Move on to Index Laws, Standard Index Form, Whole Numbers, Counting, which build directly on this idea.
Related resources
Stuck on Square Roots? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor