Year 9 Surds Worksheet — Level 2 — Practice Set 4 — 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 2 — Practice Set 4 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √72.
Answer: 6√2
- 72 = 36 × 2
- √72 = √36 × √2 = 6√2
2.Simplify 3√14 + 9√14.
Answer: 12√14
- These are like surds (both √14)
- 3 + 9 = 12, so 12√14
3.Simplify √60 + √240.
Answer: 6√15
- √60 = 2√15 and √240 = 4√15
- 2√15 + 4√15 = 6√15
4.Simplify √2 × √11.
Answer: √22
- √2 × √11 = √22
- 22 has no square factor, so √22 is simplest
5.Simplify √27.
Answer: 3√3
- 27 = 9 × 3
- √27 = √9 × √3 = 3√3
6.Simplify 3√2 + 4√2.
Answer: 7√2
- These are like surds (both √2)
- 3 + 4 = 7, so 7√2
7.Simplify √5 + √45.
Answer: 4√5
- √5 = √5 and √45 = 3√5
- √5 + 3√5 = 4√5
8.Simplify √3 × √7.
Answer: √21
- √3 × √7 = √21
- 21 has no square factor, so √21 is simplest
9.Simplify √405.
Answer: 9√5
- 405 = 81 × 5
- √405 = √81 × √5 = 9√5
10.Simplify 4√10 + 8√10.
Answer: 12√10
- These are like surds (both √10)
- 4 + 8 = 12, so 12√10
11.Simplify √96 + √150.
Answer: 9√6
- √96 = 4√6 and √150 = 5√6
- 4√6 + 5√6 = 9√6
12.Simplify √8 × √32.
Answer: 16
- √8 × √32 = √256
- = 16
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.