Year 10 Surds Worksheet — Level 1 — 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 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √45.
Answer: 3√5
- 45 = 9 × 5
- √45 = √9 × √5 = 3√5
2.Simplify √32.
Answer: 4√2
- 32 = 16 × 2
- √32 = √16 × √2 = 4√2
3.Simplify √40.
Answer: 2√10
- 40 = 4 × 10
- √40 = √4 × √10 = 2√10
4.Simplify √20.
Answer: 2√5
- 20 = 4 × 5
- √20 = √4 × √5 = 2√5
5.Simplify √54.
Answer: 3√6
- 54 = 9 × 6
- √54 = √9 × √6 = 3√6
6.Simplify √504.
Answer: 6√14
- 504 = 36 × 14
- √504 = √36 × √14 = 6√14
7.Simplify √60.
Answer: 2√15
- 60 = 4 × 15
- √60 = √4 × √15 = 2√15
8.Simplify √50.
Answer: 5√2
- 50 = 25 × 2
- √50 = √25 × √2 = 5√2
9.Simplify √117.
Answer: 3√13
- 117 = 9 × 13
- √117 = √9 × √13 = 3√13
10.Simplify √80.
Answer: 4√5
- 80 = 16 × 5
- √80 = √16 × √5 = 4√5
11.Simplify √56.
Answer: 2√14
- 56 = 4 × 14
- √56 = √4 × √14 = 2√14
12.Simplify √75.
Answer: 5√3
- 75 = 25 × 3
- √75 = √25 × √3 = 5√3
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.