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 √7 + √63.
Answer: 4√7
- √7 = √7 and √63 = 3√7
- √7 + 3√7 = 4√7
2.Simplify 6√2 × 3√15.
Answer: 18√30
- 6 × 3 = 18 and √2 × √15 = √30
- 18√30
3.Expand and simplify: √2(5 + √2)
Answer: 5√2 + 2
- √2 × 5 = 5√2
- √2 × √2 = 2
4.Rationalise the denominator:
Answer: 5√2
- Multiply top and bottom by √2:
- 10 ÷ 2 = 5, so 5√2
5.Simplify √63 + √7.
Answer: 4√7
- √63 = 3√7 and √7 = √7
- 3√7 + √7 = 4√7
6.Simplify 2√2 × 3√6.
Answer: 12√3
- 2 × 3 = 6 and √2 × √6 = √12
- √12 = 2√3, so 6 × 2√3 = 12√3
7.Expand and simplify: √2(6 + √2)
Answer: 6√2 + 2
- √2 × 6 = 6√2
- √2 × √2 = 2
8.Rationalise the denominator:
Answer: √15
- Multiply top and bottom by √15:
- 15 ÷ 15 = 1, so √15
9.Simplify √175 − √28.
Answer: 3√7
- √175 = 5√7 and √28 = 2√7
- 5√7 − 2√7 = 3√7
10.Simplify 3√2 × 2√15.
Answer: 6√30
- 3 × 2 = 6 and √2 × √15 = √30
- 6√30
11.Expand and simplify: √6(1 + √6)
Answer: √6 + 6
- √6 × 1 = √6
- √6 × √6 = 6
12.Rationalise the denominator:
Answer: √3
- Multiply top and bottom by √3:
- 3 ÷ 3 = 1, so √3
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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