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 √539.
Answer: 7√11
- 539 = 49 × 11
- √539 = √49 × √11 = 7√11
2.Simplify 4√7 − √7.
Answer: 3√7
- These are like surds (both √7)
- 4 − 1 = 3, so 3√7
3.Simplify √44 + √11.
Answer: 3√11
- √44 = 2√11 and √11 = √11
- 2√11 + √11 = 3√11
4.Simplify √3 × √7.
Answer: √21
- √3 × √7 = √21
- 21 has no square factor, so √21 is simplest
5.Simplify √52.
Answer: 2√13
- 52 = 4 × 13
- √52 = √4 × √13 = 2√13
6.Simplify 4√15 + 5√15.
Answer: 9√15
- These are like surds (both √15)
- 4 + 5 = 9, so 9√15
7.Simplify √5 + √20.
Answer: 3√5
- √5 = √5 and √20 = 2√5
- √5 + 2√5 = 3√5
8.Simplify √2 × √5.
Answer: √10
- √2 × √5 = √10
- 10 has no square factor, so √10 is simplest
9.Simplify √18.
Answer: 3√2
- 18 = 9 × 2
- √18 = √9 × √2 = 3√2
10.Simplify 2√10 + 2√10.
Answer: 4√10
- These are like surds (both √10)
- 2 + 2 = 4, so 4√10
11.Simplify √112 + √28.
Answer: 6√7
- √112 = 4√7 and √28 = 2√7
- 4√7 + 2√7 = 6√7
12.Simplify √2 × √13.
Answer: √26
- √2 × √13 = √26
- 26 has no square factor, so √26 is simplest
Marking tips
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