Year 9 Surds Worksheet — Level 2 — 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 2 — 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 √396.
Answer: 6√11
- 396 = 36 × 11
- √396 = √36 × √11 = 6√11
2.Simplify 6√6 + 9√6.
Answer: 15√6
- These are like surds (both √6)
- 6 + 9 = 15, so 15√6
3.Simplify √32 + √8.
Answer: 6√2
- √32 = 4√2 and √8 = 2√2
- 4√2 + 2√2 = 6√2
4.Simplify √52 × √117.
Answer: 78
- √52 × √117 = √6084
- √6084 = 78
5.Simplify √90.
Answer: 3√10
- 90 = 9 × 10
- √90 = √9 × √10 = 3√10
6.Simplify 2√13 + √13.
Answer: 3√13
- These are like surds (both √13)
- 2 + 1 = 3, so 3√13
7.Simplify √32 + √2.
Answer: 5√2
- √32 = 4√2 and √2 = √2
- 4√2 + √2 = 5√2
8.Simplify √6 × √24.
Answer: 12
- √6 × √24 = √144
- = 12
9.Simplify √162.
Answer: 9√2
- 162 = 81 × 2
- √162 = √81 × √2 = 9√2
10.Simplify 5√6 + 5√6.
Answer: 10√6
- These are like surds (both √6)
- 5 + 5 = 10, so 10√6
11.Simplify √40 + √90.
Answer: 5√10
- √40 = 2√10 and √90 = 3√10
- 2√10 + 3√10 = 5√10
12.Simplify √2 × √11.
Answer: √22
- √2 × √11 = √22
- 22 has no square factor, so √22 is simplest
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.
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