Year 9 Surds Worksheet — Level 3 — Practice Set 3 — 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 3 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √325 − √52.
Answer: 3√13
- √325 = 5√13 and √52 = 2√13
- 5√13 − 2√13 = 3√13
2.Simplify 6√3 × 4√6.
Answer: 72√2
- 6 × 4 = 24 and √3 × √6 = √18
- √18 = 3√2, so 24 × 3√2 = 72√2
3.Expand and simplify: √3(3 + √3)
Answer: 3√3 + 3
- √3 × 3 = 3√3
- √3 × √3 = 3
4.Rationalise the denominator:
Answer: 2√11
- Multiply top and bottom by √11:
- 22 ÷ 11 = 2, so 2√11
5.Simplify √40 + √90.
Answer: 5√10
- √40 = 2√10 and √90 = 3√10
- 2√10 + 3√10 = 5√10
6.Simplify 5√6 × 6√2.
Answer: 60√3
- 5 × 6 = 30 and √6 × √2 = √12
- √12 = 2√3, so 30 × 2√3 = 60√3
7.Expand and simplify: √15(5 + √15)
Answer: 5√15 + 15
- √15 × 5 = 5√15
- √15 × √15 = 15
8.Rationalise the denominator:
Answer: √3
- Multiply top and bottom by √3:
- 3 ÷ 3 = 1, so √3
9.Simplify √32 − √2.
Answer: 3√2
- √32 = 4√2 and √2 = √2
- 4√2 − √2 = 3√2
10.Simplify 2√2 × 2√3.
Answer: 4√6
- 2 × 2 = 4 and √2 × √3 = √6
- 4√6
11.Expand and simplify: √3(6 + √3)
Answer: 6√3 + 3
- √3 × 6 = 6√3
- √3 × √3 = 3
12.Rationalise the denominator:
Answer: 2√2
- Multiply top and bottom by √2:
- 4 ÷ 2 = 2, so 2√2
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.