Year 11 Surds Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Indices & Scientific NotationYear 11 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 √63.
Answer: 3√7
- 63 = 9 × 7
- √63 = √9 × √7 = 3√7
2.Simplify 8√6 + 3√6.
Answer: 11√6
- These are like surds (both √6)
- 8 + 3 = 11, so 11√6
3.Simplify √126 + √224.
Answer: 7√14
- √126 = 3√14 and √224 = 4√14
- 3√14 + 4√14 = 7√14
4.Simplify √2 × √7.
Answer: √14
- √2 × √7 = √14
- 14 has no square factor, so √14 is simplest
5.Simplify √539.
Answer: 7√11
- 539 = 49 × 11
- √539 = √49 × √11 = 7√11
6.Simplify 4√13 + 7√13.
Answer: 11√13
- These are like surds (both √13)
- 4 + 7 = 11, so 11√13
7.Simplify √44 + √99.
Answer: 5√11
- √44 = 2√11 and √99 = 3√11
- 2√11 + 3√11 = 5√11
8.Simplify √2 × √5.
Answer: √10
- √2 × √5 = √10
- 10 has no square factor, so √10 is simplest
9.Simplify √384.
Answer: 8√6
- 384 = 64 × 6
- √384 = √64 × √6 = 8√6
10.Simplify 6√15 + 3√15.
Answer: 9√15
- These are like surds (both √15)
- 6 + 3 = 9, so 9√15
11.Simplify √50 + √2.
Answer: 6√2
- √50 = 5√2 and √2 = √2
- 5√2 + √2 = 6√2
12.Simplify √2 × √3.
Answer: √6
- √2 × √3 = √6
- 6 has no square factor, so √6 is simplest
Marking tips
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