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 √960.
Answer: 8√15
- 960 = 64 × 15
- √960 = √64 × √15 = 8√15
2.Simplify 6√11 + 7√11.
Answer: 13√11
- These are like surds (both √11)
- 6 + 7 = 13, so 13√11
3.Simplify √150 + √216.
Answer: 11√6
- √150 = 5√6 and √216 = 6√6
- 5√6 + 6√6 = 11√6
4.Simplify √2 × √3.
Answer: √6
- √2 × √3 = √6
- 6 has no square factor, so √6 is simplest
5.Simplify √1500.
Answer: 10√15
- 1500 = 100 × 15
- √1500 = √100 × √15 = 10√15
6.Simplify 8√2 − 3√2.
Answer: 5√2
- These are like surds (both √2)
- 8 − 3 = 5, so 5√2
7.Simplify √117 + √325.
Answer: 8√13
- √117 = 3√13 and √325 = 5√13
- 3√13 + 5√13 = 8√13
8.Simplify √3 × √13.
Answer: √39
- √3 × √13 = √39
- 39 has no square factor, so √39 is simplest
9.Simplify √75.
Answer: 5√3
- 75 = 25 × 3
- √75 = √25 × √3 = 5√3
10.Simplify 8√14 − 7√14.
Answer: √14
- These are like surds (both √14)
- 8 − 7 = 1, so √14
11.Simplify √20 + √80.
Answer: 6√5
- √20 = 2√5 and √80 = 4√5
- 2√5 + 4√5 = 6√5
12.Simplify √54 × √6.
Answer: 18
- √54 × √6 = √324
- √324 = 18
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.