Year 11 Surds Worksheet — Level 2 — Practice Set 2 — 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 2 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √63.
Answer: 3√7
- 63 = 9 × 7
- √63 = √9 × √7 = 3√7
2.Simplify 7√13 − 5√13.
Answer: 2√13
- These are like surds (both √13)
- 7 − 5 = 2, so 2√13
3.Simplify √5 + √45.
Answer: 4√5
- √5 = √5 and √45 = 3√5
- √5 + 3√5 = 4√5
4.Simplify √3 × √7.
Answer: √21
- √3 × √7 = √21
- 21 has no square factor, so √21 is simplest
5.Simplify √44.
Answer: 2√11
- 44 = 4 × 11
- √44 = √4 × √11 = 2√11
6.Simplify 5√2 + 7√2.
Answer: 12√2
- These are like surds (both √2)
- 5 + 7 = 12, so 12√2
7.Simplify √240 + √135.
Answer: 7√15
- √240 = 4√15 and √135 = 3√15
- 4√15 + 3√15 = 7√15
8.Simplify √5 × √7.
Answer: √35
- √5 × √7 = √35
- 35 has no square factor, so √35 is simplest
9.Simplify √32.
Answer: 4√2
- 32 = 16 × 2
- √32 = √16 × √2 = 4√2
10.Simplify 4√6 + √6.
Answer: 5√6
- These are like surds (both √6)
- 4 + 1 = 5, so 5√6
11.Simplify √28 + √112.
Answer: 6√7
- √28 = 2√7 and √112 = 4√7
- 2√7 + 4√7 = 6√7
12.Simplify √44 × √176.
Answer: 88
- √44 × √176 = √7744
- √7744 = 88
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.