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 √375 − √15.
Answer: 4√15
- √375 = 5√15 and √15 = √15
- 5√15 − √15 = 4√15
2.Simplify 2√5 × 3√6.
Answer: 6√30
- 2 × 3 = 6 and √5 × √6 = √30
- 6√30
3.Expand and simplify: √13(1 + √13)
Answer: √13 + 13
- √13 × 1 = √13
- √13 × √13 = 13
4.Rationalise the denominator:
Answer: 6√15
- Multiply top and bottom by √15:
- 90 ÷ 15 = 6, so 6√15
5.Simplify √125 − √80.
Answer: √5
- √125 = 5√5 and √80 = 4√5
- 5√5 − 4√5 = √5
6.Simplify 3√5 × 2√6.
Answer: 6√30
- 3 × 2 = 6 and √5 × √6 = √30
- 6√30
7.Expand and simplify: √10(6 + √10)
Answer: 6√10 + 10
- √10 × 6 = 6√10
- √10 × √10 = 10
8.Rationalise the denominator:
Answer: √10
- Multiply top and bottom by √10:
- 10 ÷ 10 = 1, so √10
9.Simplify √117 + √208.
Answer: 7√13
- √117 = 3√13 and √208 = 4√13
- 3√13 + 4√13 = 7√13
10.Simplify 2√6 × 6√6.
Answer: 72
- 2 × 6 = 12 and √6 × √6 = √36
- √36 = 6, so 12 × 6 = 72
11.Expand and simplify: √2(4 + √2)
Answer: 4√2 + 2
- √2 × 4 = 4√2
- √2 × √2 = 2
12.Rationalise the denominator:
Answer: 5√11
- Multiply top and bottom by √11:
- 55 ÷ 11 = 5, so 5√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.