Year 10 Surds Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 10 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Indices & Scientific NotationYear 10 Surds Worksheet — Level 1 — Practice Set 3 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √216.
Answer: 6√6
- 216 = 36 × 6
- √216 = √36 × √6 = 6√6
2.Simplify √24.
Answer: 2√6
- 24 = 4 × 6
- √24 = √4 × √6 = 2√6
3.Simplify √50.
Answer: 5√2
- 50 = 25 × 2
- √50 = √25 × √2 = 5√2
4.Simplify √18.
Answer: 3√2
- 18 = 9 × 2
- √18 = √9 × √2 = 3√2
5.Simplify √108.
Answer: 6√3
- 108 = 36 × 3
- √108 = √36 × √3 = 6√3
6.Simplify √20.
Answer: 2√5
- 20 = 4 × 5
- √20 = √4 × √5 = 2√5
7.Simplify √12.
Answer: 2√3
- 12 = 4 × 3
- √12 = √4 × √3 = 2√3
8.Simplify √52.
Answer: 2√13
- 52 = 4 × 13
- √52 = √4 × √13 = 2√13
9.Simplify √54.
Answer: 3√6
- 54 = 9 × 6
- √54 = √9 × √6 = 3√6
10.Simplify √160.
Answer: 4√10
- 160 = 16 × 10
- √160 = √16 × √10 = 4√10
11.Simplify √32.
Answer: 4√2
- 32 = 16 × 2
- √32 = √16 × √2 = 4√2
12.Simplify √8.
Answer: 2√2
- 8 = 4 × 2
- √8 = √4 × √2 = 2√2
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.