Year 11 Surds Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √24 + √54.
Answer: 5√6
- √24 = 2√6 and √54 = 3√6
- 2√6 + 3√6 = 5√6
2.Simplify 3√2 × 5√6.
Answer: 30√3
- 3 × 5 = 15 and √2 × √6 = √12
- √12 = 2√3, so 15 × 2√3 = 30√3
3.Expand and simplify: √5(7 + √5)
Answer: 7√5 + 5
- √5 × 7 = 7√5
- √5 × √5 = 5
4.Rationalise the denominator:
Answer: 6√11
- Multiply top and bottom by √11:
- 66 ÷ 11 = 6, so 6√11
5.Simplify √54 + √6.
Answer: 4√6
- √54 = 3√6 and √6 = √6
- 3√6 + √6 = 4√6
6.Simplify 4√5 × 2√2.
Answer: 8√10
- 4 × 2 = 8 and √5 × √2 = √10
- 8√10
7.Expand and simplify: √13(8 + √13)
Answer: 8√13 + 13
- √13 × 8 = 8√13
- √13 × √13 = 13
8.Rationalise the denominator:
Answer: 6√10
- Multiply top and bottom by √10:
- 60 ÷ 10 = 6, so 6√10
9.Simplify √20 − √5.
Answer: √5
- √20 = 2√5 and √5 = √5
- 2√5 − √5 = √5
10.Simplify 6√5 × 5√10.
Answer: 150√2
- 6 × 5 = 30 and √5 × √10 = √50
- √50 = 5√2, so 30 × 5√2 = 150√2
11.Expand and simplify: √14(4 + √14)
Answer: 4√14 + 14
- √14 × 4 = 4√14
- √14 × √14 = 14
12.Rationalise the denominator:
Answer: √6
- Multiply top and bottom by √6:
- 6 ÷ 6 = 1, so √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.