Year 10 Surds Worksheet — Level 3 — 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 3 — 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 √275 + √11.
Answer: 6√11
- √275 = 5√11 and √11 = √11
- 5√11 + √11 = 6√11
2.Simplify 3√3 × 3√2.
Answer: 9√6
- 3 × 3 = 9 and √3 × √2 = √6
- 9√6
3.Expand and simplify: √3(3 + √3)
Answer: 3√3 + 3
- √3 × 3 = 3√3
- √3 × √3 = 3
4.Rationalise the denominator:
Answer: 4√14
- Multiply top and bottom by √14:
- 56 ÷ 14 = 4, so 4√14
5.Simplify √96 − √54.
Answer: √6
- √96 = 4√6 and √54 = 3√6
- 4√6 − 3√6 = √6
6.Simplify 6√2 × 2√10.
Answer: 24√5
- 6 × 2 = 12 and √2 × √10 = √20
- √20 = 2√5, so 12 × 2√5 = 24√5
7.Expand and simplify: √7(8 + √7)
Answer: 8√7 + 7
- √7 × 8 = 8√7
- √7 × √7 = 7
8.Rationalise the denominator:
Answer: 3√7
- Multiply top and bottom by √7:
- 21 ÷ 7 = 3, so 3√7
9.Simplify √44 − √11.
Answer: √11
- √44 = 2√11 and √11 = √11
- 2√11 − √11 = √11
10.Simplify 3√2 × 3√6.
Answer: 18√3
- 3 × 3 = 9 and √2 × √6 = √12
- √12 = 2√3, so 9 × 2√3 = 18√3
11.Expand and simplify: √13(4 + √13)
Answer: 4√13 + 13
- √13 × 4 = 4√13
- √13 × √13 = 13
12.Rationalise the denominator:
Answer: 2√11
- Multiply top and bottom by √11:
- 22 ÷ 11 = 2, so 2√11
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.