Year 10 Surds Worksheet — Level 2 — Practice Set 4 — 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 4 — 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 9√3 + √3.
Answer: 10√3
- These are like surds (both √3)
- 9 + 1 = 10, so 10√3
3.Simplify √208 + √52.
Answer: 6√13
- √208 = 4√13 and √52 = 2√13
- 4√13 + 2√13 = 6√13
4.Simplify √2 × √11.
Answer: √22
- √2 × √11 = √22
- 22 has no square factor, so √22 is simplest
5.Simplify √294.
Answer: 7√6
- 294 = 49 × 6
- √294 = √49 × √6 = 7√6
6.Simplify 6√11 + 3√11.
Answer: 9√11
- These are like surds (both √11)
- 6 + 3 = 9, so 9√11
7.Simplify √15 + √135.
Answer: 4√15
- √15 = √15 and √135 = 3√15
- √15 + 3√15 = 4√15
8.Simplify √60 × √15.
Answer: 30
- √60 × √15 = √900
- √900 = 30
9.Simplify √147.
Answer: 7√3
- 147 = 49 × 3
- √147 = √49 × √3 = 7√3
10.Simplify 6√13 − √13.
Answer: 5√13
- These are like surds (both √13)
- 6 − 1 = 5, so 5√13
11.Simplify √224 + √350.
Answer: 9√14
- √224 = 4√14 and √350 = 5√14
- 4√14 + 5√14 = 9√14
12.Simplify √63 × √112.
Answer: 84
- √63 × √112 = √7056
- √7056 = 84
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.