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 √1400.
Answer: 10√14
- 1400 = 100 × 14
- √1400 = √100 × √14 = 10√14
2.Simplify 7√15 − 4√15.
Answer: 3√15
- These are like surds (both √15)
- 7 − 4 = 3, so 3√15
3.Simplify √5 + √20.
Answer: 3√5
- √5 = √5 and √20 = 2√5
- √5 + 2√5 = 3√5
4.Simplify √63 × √28.
Answer: 42
- √63 × √28 = √1764
- √1764 = 42
5.Simplify √1215.
Answer: 9√15
- 1215 = 81 × 15
- √1215 = √81 × √15 = 9√15
6.Simplify 4√13 + 7√13.
Answer: 11√13
- These are like surds (both √13)
- 4 + 7 = 11, so 11√13
7.Simplify √8 + √32.
Answer: 6√2
- √8 = 2√2 and √32 = 4√2
- 2√2 + 4√2 = 6√2
8.Simplify √24 × √6.
Answer: 12
- √24 × √6 = √144
- √144 = 12
9.Simplify √208.
Answer: 4√13
- 208 = 16 × 13
- √208 = √16 × √13 = 4√13
10.Simplify 2√3 + 5√3.
Answer: 7√3
- These are like surds (both √3)
- 2 + 5 = 7, so 7√3
11.Simplify √50 + √72.
Answer: 11√2
- √50 = 5√2 and √72 = 6√2
- 5√2 + 6√2 = 11√2
12.Simplify √11 × √99.
Answer: 33
- √11 × √99 = √1089
- √1089 = 33
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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