Year 10 Surds Worksheet — Level 2 — Practice Set 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 — Practice Set 2 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √1053.
Answer: 9√13
- 1053 = 81 × 13
- √1053 = √81 × √13 = 9√13
2.Simplify 3√11 + 8√11.
Answer: 11√11
- These are like surds (both √11)
- 3 + 8 = 11, so 11√11
3.Simplify √50 + √2.
Answer: 6√2
- √50 = 5√2 and √2 = √2
- 5√2 + √2 = 6√2
4.Simplify √5 × √7.
Answer: √35
- √5 × √7 = √35
- 35 has no square factor, so √35 is simplest
5.Simplify √40.
Answer: 2√10
- 40 = 4 × 10
- √40 = √4 × √10 = 2√10
6.Simplify 8√15 + 8√15.
Answer: 16√15
- These are like surds (both √15)
- 8 + 8 = 16, so 16√15
7.Simplify √99 + √176.
Answer: 7√11
- √99 = 3√11 and √176 = 4√11
- 3√11 + 4√11 = 7√11
8.Simplify √126 × √224.
Answer: 168
- √126 × √224 = √28224
- √28224 = 168
9.Simplify √1100.
Answer: 10√11
- 1100 = 100 × 11
- √1100 = √100 × √11 = 10√11
10.Simplify 8√2 + 5√2.
Answer: 13√2
- These are like surds (both √2)
- 8 + 5 = 13, so 13√2
11.Simplify √3 + √48.
Answer: 5√3
- √3 = √3 and √48 = 4√3
- √3 + 4√3 = 5√3
12.Simplify √2 × √7.
Answer: √14
- √2 × √7 = √14
- 14 has no square factor, so √14 is simplest
Marking tips
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