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 √60.
Answer: 2√15
- 60 = 4 × 15
- √60 = √4 × √15 = 2√15
2.Simplify 7√11 + 4√11.
Answer: 11√11
- These are like surds (both √11)
- 7 + 4 = 11, so 11√11
3.Simplify √126 + √224.
Answer: 7√14
- √126 = 3√14 and √224 = 4√14
- 3√14 + 4√14 = 7√14
4.Simplify √20 × √45.
Answer: 30
- √20 × √45 = √900
- √900 = 30
5.Simplify √360.
Answer: 6√10
- 360 = 36 × 10
- √360 = √36 × √10 = 6√10
6.Simplify 9√11 + 5√11.
Answer: 14√11
- These are like surds (both √11)
- 9 + 5 = 14, so 14√11
7.Simplify √60 + √375.
Answer: 7√15
- √60 = 2√15 and √375 = 5√15
- 2√15 + 5√15 = 7√15
8.Simplify √2 × √13.
Answer: √26
- √2 × √13 = √26
- 26 has no square factor, so √26 is simplest
9.Simplify √32.
Answer: 4√2
- 32 = 16 × 2
- √32 = √16 × √2 = 4√2
10.Simplify 8√14 + 7√14.
Answer: 15√14
- These are like surds (both √14)
- 8 + 7 = 15, so 15√14
11.Simplify √80 + √20.
Answer: 6√5
- √80 = 4√5 and √20 = 2√5
- 4√5 + 2√5 = 6√5
12.Simplify √3 × √5.
Answer: √15
- √3 × √5 = √15
- 15 has no square factor, so √15 is simplest
Marking tips
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