Year 10 Surds Worksheet — Level 2 — Practice Set 3 — 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 3 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √32.
Answer: 4√2
- 32 = 16 × 2
- √32 = √16 × √2 = 4√2
2.Simplify 9√3 − 7√3.
Answer: 2√3
- These are like surds (both √3)
- 9 − 7 = 2, so 2√3
3.Simplify √45 + √125.
Answer: 8√5
- √45 = 3√5 and √125 = 5√5
- 3√5 + 5√5 = 8√5
4.Simplify √126 × √56.
Answer: 84
- √126 × √56 = √7056
- √7056 = 84
5.Simplify √325.
Answer: 5√13
- 325 = 25 × 13
- √325 = √25 × √13 = 5√13
6.Simplify 7√14 − 5√14.
Answer: 2√14
- These are like surds (both √14)
- 7 − 5 = 2, so 2√14
7.Simplify √15 + √60.
Answer: 3√15
- √15 = √15 and √60 = 2√15
- √15 + 2√15 = 3√15
8.Simplify √3 × √11.
Answer: √33
- √3 × √11 = √33
- 33 has no square factor, so √33 is simplest
9.Simplify √90.
Answer: 3√10
- 90 = 9 × 10
- √90 = √9 × √10 = 3√10
10.Simplify 2√11 + 9√11.
Answer: 11√11
- These are like surds (both √11)
- 2 + 9 = 11, so 11√11
11.Simplify √32 + √2.
Answer: 5√2
- √32 = 4√2 and √2 = √2
- 4√2 + √2 = 5√2
12.Simplify √12 × √3.
Answer: 6
- √12 × √3 = √36
- √36 = 6
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.