Year 9 Surds Worksheet — Level 3 — Practice Set 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 — 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 √250 − √40.
Answer: 3√10
- √250 = 5√10 and √40 = 2√10
- 5√10 − 2√10 = 3√10
2.Simplify 6√5 × 3√15.
Answer: 90√3
- 6 × 3 = 18 and √5 × √15 = √75
- √75 = 5√3, so 18 × 5√3 = 90√3
3.Expand and simplify: √10(1 + √10)
Answer: √10 + 10
- √10 × 1 = √10
- √10 × √10 = 10
4.Rationalise the denominator:
Answer: √14
- Multiply top and bottom by √14:
- 14 ÷ 14 = 1, so √14
5.Simplify √175 − √7.
Answer: 4√7
- √175 = 5√7 and √7 = √7
- 5√7 − √7 = 4√7
6.Simplify 2√2 × 2√6.
Answer: 8√3
- 2 × 2 = 4 and √2 × √6 = √12
- √12 = 2√3, so 4 × 2√3 = 8√3
7.Expand and simplify: √6(2 + √6)
Answer: 2√6 + 6
- √6 × 2 = 2√6
- √6 × √6 = 6
8.Rationalise the denominator:
Answer: 4√6
- Multiply top and bottom by √6:
- 24 ÷ 6 = 4, so 4√6
9.Simplify √20 − √5.
Answer: √5
- √20 = 2√5 and √5 = √5
- 2√5 − √5 = √5
10.Simplify 3√5 × 4√15.
Answer: 60√3
- 3 × 4 = 12 and √5 × √15 = √75
- √75 = 5√3, so 12 × 5√3 = 60√3
11.Expand and simplify: √6(8 + √6)
Answer: 8√6 + 6
- √6 × 8 = 8√6
- √6 × √6 = 6
12.Rationalise the denominator:
Answer: √2
- Multiply top and bottom by √2:
- 2 ÷ 2 = 1, so √2
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.
- Celebrate what went well first, then pick one thing to work on next.