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 √350.
Answer: 5√14
- 350 = 25 × 14
- √350 = √25 × √14 = 5√14
2.Simplify 5√6 + √6.
Answer: 6√6
- These are like surds (both √6)
- 5 + 1 = 6, so 6√6
3.Simplify √208 + √52.
Answer: 6√13
- √208 = 4√13 and √52 = 2√13
- 4√13 + 2√13 = 6√13
4.Simplify √2 × √8.
Answer: 4
- √2 × √8 = √16
- √16 = 4
5.Simplify √275.
Answer: 5√11
- 275 = 25 × 11
- √275 = √25 × √11 = 5√11
6.Simplify 4√13 + 2√13.
Answer: 6√13
- These are like surds (both √13)
- 4 + 2 = 6, so 6√13
7.Simplify √275 + √11.
Answer: 6√11
- √275 = 5√11 and √11 = √11
- 5√11 + √11 = 6√11
8.Simplify √5 × √7.
Answer: √35
- √5 × √7 = √35
- 35 has no square factor, so √35 is simplest
9.Simplify √216.
Answer: 6√6
- 216 = 36 × 6
- √216 = √36 × √6 = 6√6
10.Simplify 5√5 + 5√5.
Answer: 10√5
- These are like surds (both √5)
- 5 + 5 = 10, so 10√5
11.Simplify √126 + √14.
Answer: 4√14
- √126 = 3√14 and √14 = √14
- 3√14 + √14 = 4√14
12.Simplify √54 × √96.
Answer: 72
- √54 × √96 = √5184
- √5184 = 72
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.