Year 10 Surds Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 10 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Indices & Scientific NotationYear 10 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 √384.
Answer: 8√6
- 384 = 64 × 6
- √384 = √64 × √6 = 8√6
2.Simplify 3√13 + 5√13.
Answer: 8√13
- These are like surds (both √13)
- 3 + 5 = 8, so 8√13
3.Simplify √224 + √350.
Answer: 9√14
- √224 = 4√14 and √350 = 5√14
- 4√14 + 5√14 = 9√14
4.Simplify √40 × √160.
Answer: 80
- √40 × √160 = √6400
- = 80
5.Simplify √99.
Answer: 3√11
- 99 = 9 × 11
- √99 = √9 × √11 = 3√11
6.Simplify 3√15 + 6√15.
Answer: 9√15
- These are like surds (both √15)
- 3 + 6 = 9, so 9√15
7.Simplify √54 + √150.
Answer: 8√6
- √54 = 3√6 and √150 = 5√6
- 3√6 + 5√6 = 8√6
8.Simplify √11 × √99.
Answer: 33
- √11 × √99 = √1089
- √1089 = 33
9.Simplify √162.
Answer: 9√2
- 162 = 81 × 2
- √162 = √81 × √2 = 9√2
10.Simplify 8√10 + √10.
Answer: 9√10
- These are like surds (both √10)
- 8 + 1 = 9, so 9√10
11.Simplify √60 + √135.
Answer: 5√15
- √60 = 2√15 and √135 = 3√15
- 2√15 + 3√15 = 5√15
12.Simplify √90 × √10.
Answer: 30
- √90 × √10 = √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.