Year 9 Surds Worksheet — Level 3 — 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 3 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √240 − √60.
Answer: 2√15
- √240 = 4√15 and √60 = 2√15
- 4√15 − 2√15 = 2√15
2.Simplify 4√5 × 6√3.
Answer: 24√15
- 4 × 6 = 24 and √5 × √3 = √15
- 24√15
3.Expand and simplify: √2(3 + √2)
Answer: 3√2 + 2
- √2 × 3 = 3√2
- √2 × √2 = 2
4.Rationalise the denominator:
Answer: 6√3
- Multiply top and bottom by √3:
- 18 ÷ 3 = 6, so 6√3
5.Simplify √40 + √250.
Answer: 7√10
- √40 = 2√10 and √250 = 5√10
- 2√10 + 5√10 = 7√10
6.Simplify 4√5 × 3√2.
Answer: 12√10
- 4 × 3 = 12 and √5 × √2 = √10
- 12√10
7.Expand and simplify: √6(3 + √6)
Answer: 3√6 + 6
- √6 × 3 = 3√6
- √6 × √6 = 6
8.Rationalise the denominator:
Answer: 6√2
- Multiply top and bottom by √2:
- 12 ÷ 2 = 6, so 6√2
9.Simplify √224 − √56.
Answer: 2√14
- √224 = 4√14 and √56 = 2√14
- 4√14 − 2√14 = 2√14
10.Simplify 5√6 × 4√6.
Answer: 120
- 5 × 4 = 20 and √6 × √6 = √36
- √36 = 6, so 20 × 6 = 120
11.Expand and simplify: √7(1 + √7)
Answer: √7 + 7
- √7 × 1 = √7
- √7 × √7 = 7
12.Rationalise the denominator:
Answer: 2√5
- Multiply top and bottom by √5:
- 10 ÷ 5 = 2, so 2√5
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
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