Year 9 Surds Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √80 − √45.
Answer: √5
- √80 = 4√5 and √45 = 3√5
- 4√5 − 3√5 = √5
2.Simplify 5√6 × 5√10.
Answer: 50√15
- 5 × 5 = 25 and √6 × √10 = √60
- √60 = 2√15, so 25 × 2√15 = 50√15
3.Expand and simplify: √10(6 + √10)
Answer: 6√10 + 10
- √10 × 6 = 6√10
- √10 × √10 = 10
4.Rationalise the denominator:
Answer: 4√3
- Multiply top and bottom by √3:
- 12 ÷ 3 = 4, so 4√3
5.Simplify √208 + √325.
Answer: 9√13
- √208 = 4√13 and √325 = 5√13
- 4√13 + 5√13 = 9√13
6.Simplify 5√2 × 2√3.
Answer: 10√6
- 5 × 2 = 10 and √2 × √3 = √6
- 10√6
7.Expand and simplify: √6(1 + √6)
Answer: √6 + 6
- √6 × 1 = √6
- √6 × √6 = 6
8.Rationalise the denominator:
Answer: 4√7
- Multiply top and bottom by √7:
- 28 ÷ 7 = 4, so 4√7
9.Simplify √250 − √10.
Answer: 4√10
- √250 = 5√10 and √10 = √10
- 5√10 − √10 = 4√10
10.Simplify 5√2 × 6√2.
Answer: 60
- 5 × 6 = 30 and √2 × √2 = √4
- √4 = 2, so 30 × 2 = 60
11.Expand and simplify: √7(1 + √7)
Answer: √7 + 7
- √7 × 1 = √7
- √7 × √7 = 7
12.Rationalise the denominator:
Answer: 6√6
- Multiply top and bottom by √6:
- 36 ÷ 6 = 6, so 6√6
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.