Year 9 Surds Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 9 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Indices & Scientific NotationYear 9 Surds Worksheet — Level 2 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √1215.
Answer: 9√15
- 1215 = 81 × 15
- √1215 = √81 × √15 = 9√15
2.Simplify 9√3 + √3.
Answer: 10√3
- These are like surds (both √3)
- 9 + 1 = 10, so 10√3
3.Simplify √135 + √375.
Answer: 8√15
- √135 = 3√15 and √375 = 5√15
- 3√15 + 5√15 = 8√15
4.Simplify √6 × √54.
Answer: 18
- √6 × √54 = √324
- √324 = 18
5.Simplify √960.
Answer: 8√15
- 960 = 64 × 15
- √960 = √64 × √15 = 8√15
6.Simplify 4√11 + 8√11.
Answer: 12√11
- These are like surds (both √11)
- 4 + 8 = 12, so 12√11
7.Simplify √126 + √224.
Answer: 7√14
- √126 = 3√14 and √224 = 4√14
- 3√14 + 4√14 = 7√14
8.Simplify √2 × √13.
Answer: √26
- √2 × √13 = √26
- 26 has no square factor, so √26 is simplest
9.Simplify √52.
Answer: 2√13
- 52 = 4 × 13
- √52 = √4 × √13 = 2√13
10.Simplify 3√11 + 3√11.
Answer: 6√11
- These are like surds (both √11)
- 3 + 3 = 6, so 6√11
11.Simplify √2 + √50.
Answer: 6√2
- √2 = √2 and √50 = 5√2
- √2 + 5√2 = 6√2
12.Simplify √126 × √56.
Answer: 84
- √126 × √56 = √7056
- √7056 = 84
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.