Year 10 Surds Worksheet — Level 3 — Practice Set 4 — 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 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 √350 − √224.
Answer: √14
- √350 = 5√14 and √224 = 4√14
- 5√14 − 4√14 = √14
2.Simplify 5√2 × 5√15.
Answer: 25√30
- 5 × 5 = 25 and √2 × √15 = √30
- 25√30
3.Expand and simplify: √10(7 + √10)
Answer: 7√10 + 10
- √10 × 7 = 7√10
- √10 × √10 = 10
4.Rationalise the denominator:
Answer: √3
- Multiply top and bottom by √3:
- 3 ÷ 3 = 1, so √3
5.Simplify √112 − √63.
Answer: √7
- √112 = 4√7 and √63 = 3√7
- 4√7 − 3√7 = √7
6.Simplify 5√6 × 2√6.
Answer: 60
- 5 × 2 = 10 and √6 × √6 = √36
- √36 = 6, so 10 × 6 = 60
7.Expand and simplify: √10(9 + √10)
Answer: 9√10 + 10
- √10 × 9 = 9√10
- √10 × √10 = 10
8.Rationalise the denominator:
Answer: 5√5
- Multiply top and bottom by √5:
- 25 ÷ 5 = 5, so 5√5
9.Simplify √135 + √240.
Answer: 7√15
- √135 = 3√15 and √240 = 4√15
- 3√15 + 4√15 = 7√15
10.Simplify 3√6 × 6√10.
Answer: 36√15
- 3 × 6 = 18 and √6 × √10 = √60
- √60 = 2√15, so 18 × 2√15 = 36√15
11.Expand and simplify: √3(9 + √3)
Answer: 9√3 + 3
- √3 × 9 = 9√3
- √3 × √3 = 3
12.Rationalise the denominator:
Answer: 2√7
- Multiply top and bottom by √7:
- 14 ÷ 7 = 2, so 2√7
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.