Year 10 Surds Worksheet — Level 3 — 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 3 — 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 √32 + √8.
Answer: 6√2
- √32 = 4√2 and √8 = 2√2
- 4√2 + 2√2 = 6√2
2.Simplify 3√6 × 3√10.
Answer: 18√15
- 3 × 3 = 9 and √6 × √10 = √60
- √60 = 2√15, so 9 × 2√15 = 18√15
3.Expand and simplify: √6(5 + √6)
Answer: 5√6 + 6
- √6 × 5 = 5√6
- √6 × √6 = 6
4.Rationalise the denominator:
Answer: √7
- Multiply top and bottom by √7:
- 7 ÷ 7 = 1, so √7
5.Simplify √63 + √7.
Answer: 4√7
- √63 = 3√7 and √7 = √7
- 3√7 + √7 = 4√7
6.Simplify 2√6 × 6√2.
Answer: 24√3
- 2 × 6 = 12 and √6 × √2 = √12
- √12 = 2√3, so 12 × 2√3 = 24√3
7.Expand and simplify: √13(8 + √13)
Answer: 8√13 + 13
- √13 × 8 = 8√13
- √13 × √13 = 13
8.Rationalise the denominator:
Answer: 6√2
- Multiply top and bottom by √2:
- 12 ÷ 2 = 6, so 6√2
9.Simplify √160 + √40.
Answer: 6√10
- √160 = 4√10 and √40 = 2√10
- 4√10 + 2√10 = 6√10
10.Simplify 3√3 × 2√10.
Answer: 6√30
- 3 × 2 = 6 and √3 × √10 = √30
- 6√30
11.Expand and simplify: √3(3 + √3)
Answer: 3√3 + 3
- √3 × 3 = 3√3
- √3 × √3 = 3
12.Rationalise the denominator:
Answer: 2√13
- Multiply top and bottom by √13:
- 26 ÷ 13 = 2, so 2√13
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.