Year 11 Surds Worksheet — Level 2 — 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 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √891.
Answer: 9√11
- 891 = 81 × 11
- √891 = √81 × √11 = 9√11
2.Simplify 2√5 + 6√5.
Answer: 8√5
- These are like surds (both √5)
- 2 + 6 = 8, so 8√5
3.Simplify √40 + √90.
Answer: 5√10
- √40 = 2√10 and √90 = 3√10
- 2√10 + 3√10 = 5√10
4.Simplify √5 × √7.
Answer: √35
- √5 × √7 = √35
- 35 has no square factor, so √35 is simplest
5.Simplify √12.
Answer: 2√3
- 12 = 4 × 3
- √12 = √4 × √3 = 2√3
6.Simplify 9√3 − 7√3.
Answer: 2√3
- These are like surds (both √3)
- 9 − 7 = 2, so 2√3
7.Simplify √15 + √240.
Answer: 5√15
- √15 = √15 and √240 = 4√15
- √15 + 4√15 = 5√15
8.Simplify √63 × √112.
Answer: 84
- √63 × √112 = √7056
- √7056 = 84
9.Simplify √117.
Answer: 3√13
- 117 = 9 × 13
- √117 = √9 × √13 = 3√13
10.Simplify 4√13 + 3√13.
Answer: 7√13
- These are like surds (both √13)
- 4 + 3 = 7, so 7√13
11.Simplify √275 + √176.
Answer: 9√11
- √275 = 5√11 and √176 = 4√11
- 5√11 + 4√11 = 9√11
12.Simplify √3 × √5.
Answer: √15
- √3 × √5 = √15
- 15 has no square factor, so √15 is simplest
Marking tips
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