Year 9 Surds Worksheet — Level 2 — Practice Set 3 — 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 3 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √360.
Answer: 6√10
- 360 = 36 × 10
- √360 = √36 × √10 = 6√10
2.Simplify 5√15 − 2√15.
Answer: 3√15
- These are like surds (both √15)
- 5 − 2 = 3, so 3√15
3.Simplify √14 + √56.
Answer: 3√14
- √14 = √14 and √56 = 2√14
- √14 + 2√14 = 3√14
4.Simplify √52 × √117.
Answer: 78
- √52 × √117 = √6084
- √6084 = 78
5.Simplify √80.
Answer: 4√5
- 80 = 16 × 5
- √80 = √16 × √5 = 4√5
6.Simplify 9√3 − √3.
Answer: 8√3
- These are like surds (both √3)
- 9 − 1 = 8, so 8√3
7.Simplify √40 + √10.
Answer: 3√10
- √40 = 2√10 and √10 = √10
- 2√10 + √10 = 3√10
8.Simplify √6 × √96.
Answer: 24
- √6 × √96 = √576
- √576 = 24
9.Simplify √32.
Answer: 4√2
- 32 = 16 × 2
- √32 = √16 × √2 = 4√2
10.Simplify 5√6 + 5√6.
Answer: 10√6
- These are like surds (both √6)
- 5 + 5 = 10, so 10√6
11.Simplify √48 + √75.
Answer: 9√3
- √48 = 4√3 and √75 = 5√3
- 4√3 + 5√3 = 9√3
12.Simplify √135 × √240.
Answer: 180
- √135 × √240 = √32400
- √32400 = 180
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.