Year 10 Surds Worksheet — Level 2 — Practice Set 3 — 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 3 — 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 8√5 + 4√5.
Answer: 12√5
- These are like surds (both √5)
- 8 + 4 = 12, so 12√5
3.Simplify √11 + √44.
Answer: 3√11
- √11 = √11 and √44 = 2√11
- √11 + 2√11 = 3√11
4.Simplify √11 × √44.
Answer: 22
- √11 × √44 = √484
- √484 = 22
5.Simplify √1500.
Answer: 10√15
- 1500 = 100 × 15
- √1500 = √100 × √15 = 10√15
6.Simplify 8√6 − 7√6.
Answer: √6
- These are like surds (both √6)
- 8 − 7 = 1, so √6
7.Simplify √18 + √2.
Answer: 4√2
- √18 = 3√2 and √2 = √2
- 3√2 + √2 = 4√2
8.Simplify √2 × √3.
Answer: √6
- √2 × √3 = √6
- 6 has no square factor, so √6 is simplest
9.Simplify √160.
Answer: 4√10
- 160 = 16 × 10
- √160 = √16 × √10 = 4√10
10.Simplify 5√10 + 2√10.
Answer: 7√10
- These are like surds (both √10)
- 5 + 2 = 7, so 7√10
11.Simplify √375 + √60.
Answer: 7√15
- √375 = 5√15 and √60 = 2√15
- 5√15 + 2√15 = 7√15
12.Simplify √2 × √11.
Answer: √22
- √2 × √11 = √22
- 22 has no square factor, so √22 is simplest
Marking tips
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