Year 9 Surds Worksheet — Level 2 — Practice Set 2 — 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 2 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √108.
Answer: 6√3
- 108 = 36 × 3
- √108 = √36 × √3 = 6√3
2.Simplify 7√15 + 9√15.
Answer: 16√15
- These are like surds (both √15)
- 7 + 9 = 16, so 16√15
3.Simplify √126 + √224.
Answer: 7√14
- √126 = 3√14 and √224 = 4√14
- 3√14 + 4√14 = 7√14
4.Simplify √2 × √18.
Answer: 6
- √2 × √18 = √36
- √36 = 6
5.Simplify √1500.
Answer: 10√15
- 1500 = 100 × 15
- √1500 = √100 × √15 = 10√15
6.Simplify 6√10 + √10.
Answer: 7√10
- These are like surds (both √10)
- 6 + 1 = 7, so 7√10
7.Simplify √224 + √56.
Answer: 6√14
- √224 = 4√14 and √56 = 2√14
- 4√14 + 2√14 = 6√14
8.Simplify √40 × √160.
Answer: 80
- √40 × √160 = √6400
- √6400 = 80
9.Simplify √18.
Answer: 3√2
- 18 = 9 × 2
- √18 = √9 × √2 = 3√2
10.Simplify 9√2 + 8√2.
Answer: 17√2
- These are like surds (both √2)
- 9 + 8 = 17, so 17√2
11.Simplify √175 + √63.
Answer: 8√7
- √175 = 5√7 and √63 = 3√7
- 5√7 + 3√7 = 8√7
12.Simplify √3 × √7.
Answer: √21
- √3 × √7 = √21
- 21 has no square factor, so √21 is simplest
Marking tips
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