Year 9 Surds Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 9 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Indices & Scientific NotationYear 9 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 √175 + √252.
Answer: 11√7
- √175 = 5√7 and √252 = 6√7
- 5√7 + 6√7 = 11√7
2.Simplify 5√6 × 4√6.
Answer: 120
- 5 × 4 = 20 and √6 × √6 = √36
- √36 = 6, so 20 × 6 = 120
3.Expand and simplify: √5(3 + √5)
Answer: 3√5 + 5
- √5 × 3 = 3√5
- √5 × √5 = 5
4.Rationalise the denominator:
Answer: 2√10
- Multiply top and bottom by √10:
- 20 ÷ 10 = 2, so 2√10
5.Simplify √18 + √8.
Answer: 5√2
- √18 = 3√2 and √8 = 2√2
- 3√2 + 2√2 = 5√2
6.Simplify 2√2 × 2√2.
Answer: 8
- 2 × 2 = 4 and √2 × √2 = √4
- √4 = 2, so 4 × 2 = 8
7.Expand and simplify: √3(1 + √3)
Answer: √3 + 3
- √3 × 1 = √3
- √3 × √3 = 3
8.Rationalise the denominator:
Answer: 4√3
- Multiply top and bottom by √3:
- 12 ÷ 3 = 4, so 4√3
9.Simplify √117 − √52.
Answer: √13
- √117 = 3√13 and √52 = 2√13
- 3√13 − 2√13 = √13
10.Simplify 3√2 × 5√6.
Answer: 30√3
- 3 × 5 = 15 and √2 × √6 = √12
- √12 = 2√3, so 15 × 2√3 = 30√3
11.Expand and simplify: √15(2 + √15)
Answer: 2√15 + 15
- √15 × 2 = 2√15
- √15 × √15 = 15
12.Rationalise the denominator:
Answer: 5√3
- Multiply top and bottom by √3:
- 15 ÷ 3 = 5, so 5√3
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.