Year 10 Surds Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 10 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Indices & Scientific NotationYear 10 Surds Worksheet — Level 2 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √832.
Answer: 8√13
- 832 = 64 × 13
- √832 = √64 × √13 = 8√13
2.Simplify 6√5 − √5.
Answer: 5√5
- These are like surds (both √5)
- 6 − 1 = 5, so 5√5
3.Simplify √80 + √45.
Answer: 7√5
- √80 = 4√5 and √45 = 3√5
- 4√5 + 3√5 = 7√5
4.Simplify √40 × √160.
Answer: 80
- √40 × √160 = √6400
- √6400 = 80
5.Simplify √567.
Answer: 9√7
- 567 = 81 × 7
- √567 = √81 × √7 = 9√7
6.Simplify 6√3 − 2√3.
Answer: 4√3
- These are like surds (both √3)
- 6 − 2 = 4, so 4√3
7.Simplify √125 + √45.
Answer: 8√5
- √125 = 5√5 and √45 = 3√5
- 5√5 + 3√5 = 8√5
8.Simplify √10 × √40.
Answer: 20
- √10 × √40 = √400
- √400 = 20
9.Simplify √294.
Answer: 7√6
- 294 = 49 × 6
- √294 = √49 × √6 = 7√6
10.Simplify 6√6 + 7√6.
Answer: 13√6
- These are like surds (both √6)
- 6 + 7 = 13, so 13√6
11.Simplify √176 + √275.
Answer: 9√11
- √176 = 4√11 and √275 = 5√11
- 4√11 + 5√11 = 9√11
12.Simplify √3 × √12.
Answer: 6
- √3 × √12 = √36
- = 6
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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