Year 9 Surds Worksheet — Level 2 — Practice Set 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 — 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 √192.
Answer: 8√3
- 192 = 64 × 3
- √192 = √64 × √3 = 8√3
2.Simplify 5√6 + 3√6.
Answer: 8√6
- These are like surds (both √6)
- 5 + 3 = 8, so 8√6
3.Simplify √6 + √150.
Answer: 6√6
- √6 = √6 and √150 = 5√6
- √6 + 5√6 = 6√6
4.Simplify √11 × √176.
Answer: 44
- √11 × √176 = √1936
- √1936 = 44
5.Simplify √108.
Answer: 6√3
- 108 = 36 × 3
- √108 = √36 × √3 = 6√3
6.Simplify 3√14 + 3√14.
Answer: 6√14
- These are like surds (both √14)
- 3 + 3 = 6, so 6√14
7.Simplify √2 + √8.
Answer: 3√2
- √2 = √2 and √8 = 2√2
- √2 + 2√2 = 3√2
8.Simplify √2 × √3.
Answer: √6
- √2 × √3 = √6
- 6 has no square factor, so √6 is simplest
9.Simplify √700.
Answer: 10√7
- 700 = 100 × 7
- √700 = √100 × √7 = 10√7
10.Simplify 9√15 − 8√15.
Answer: √15
- These are like surds (both √15)
- 9 − 8 = 1, so √15
11.Simplify √176 + √11.
Answer: 5√11
- √176 = 4√11 and √11 = √11
- 4√11 + √11 = 5√11
12.Simplify √63 × √7.
Answer: 21
- √63 × √7 = √441
- √441 = 21
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.