Year 11 Surds Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Indices & Scientific NotationYear 11 Surds Worksheet — Level 2 — 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 √90.
Answer: 3√10
- 90 = 9 × 10
- √90 = √9 × √10 = 3√10
2.Simplify 9√6 − 4√6.
Answer: 5√6
- These are like surds (both √6)
- 9 − 4 = 5, so 5√6
3.Simplify √40 + √250.
Answer: 7√10
- √40 = 2√10 and √250 = 5√10
- 2√10 + 5√10 = 7√10
4.Simplify √28 × √63.
Answer: 42
- √28 × √63 = √1764
- √1764 = 42
5.Simplify √250.
Answer: 5√10
- 250 = 25 × 10
- √250 = √25 × √10 = 5√10
6.Simplify 8√11 + 3√11.
Answer: 11√11
- These are like surds (both √11)
- 8 + 3 = 11, so 11√11
7.Simplify √240 + √375.
Answer: 9√15
- √240 = 4√15 and √375 = 5√15
- 4√15 + 5√15 = 9√15
8.Simplify √126 × √14.
Answer: 42
- √126 × √14 = √1764
- √1764 = 42
9.Simplify √117.
Answer: 3√13
- 117 = 9 × 13
- √117 = √9 × √13 = 3√13
10.Simplify 9√3 − 8√3.
Answer: √3
- These are like surds (both √3)
- 9 − 8 = 1, so √3
11.Simplify √75 + √3.
Answer: 6√3
- √75 = 5√3 and √3 = √3
- 5√3 + √3 = 6√3
12.Simplify √15 × √60.
Answer: 30
- √15 × √60 = √900
- √900 = 30
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.