Year 11 Surds Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Indices & Scientific NotationYear 11 Surds Worksheet — Level 3 — 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 √13 + √52.
Answer: 3√13
- √13 = √13 and √52 = 2√13
- √13 + 2√13 = 3√13
2.Simplify 6√6 × 4√2.
Answer: 48√3
- 6 × 4 = 24 and √6 × √2 = √12
- √12 = 2√3, so 24 × 2√3 = 48√3
3.Expand and simplify: √15(8 + √15)
Answer: 8√15 + 15
- √15 × 8 = 8√15
- √15 × √15 = 15
4.Rationalise the denominator:
Answer: 4√15
- Multiply top and bottom by √15:
- 60 ÷ 15 = 4, so 4√15
5.Simplify √175 − √28.
Answer: 3√7
- √175 = 5√7 and √28 = 2√7
- 5√7 − 2√7 = 3√7
6.Simplify 5√2 × 2√3.
Answer: 10√6
- 5 × 2 = 10 and √2 × √3 = √6
- 10√6
7.Expand and simplify: √14(6 + √14)
Answer: 6√14 + 14
- √14 × 6 = 6√14
- √14 × √14 = 14
8.Rationalise the denominator:
Answer: 3√14
- Multiply top and bottom by √14:
- 42 ÷ 14 = 3, so 3√14
9.Simplify √325 − √208.
Answer: √13
- √325 = 5√13 and √208 = 4√13
- 5√13 − 4√13 = √13
10.Simplify 6√3 × 3√10.
Answer: 18√30
- 6 × 3 = 18 and √3 × √10 = √30
- 18√30
11.Expand and simplify: √3(7 + √3)
Answer: 7√3 + 3
- √3 × 7 = 7√3
- √3 × √3 = 3
12.Rationalise the denominator:
Answer: 3√10
- Multiply top and bottom by √10:
- 30 ÷ 10 = 3, so 3√10
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.