Year 10 Surds Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √126 − √14.
Answer: 2√14
- √126 = 3√14 and √14 = √14
- 3√14 − √14 = 2√14
2.Simplify 6√6 × 2√15.
Answer: 36√10
- 6 × 2 = 12 and √6 × √15 = √90
- √90 = 3√10, so 12 × 3√10 = 36√10
3.Expand and simplify: √6(5 + √6)
Answer: 5√6 + 6
- √6 × 5 = 5√6
- √6 × √6 = 6
4.Rationalise the denominator:
Answer: 6√14
- Multiply top and bottom by √14:
- 84 ÷ 14 = 6, so 6√14
5.Simplify √150 + √54.
Answer: 8√6
- √150 = 5√6 and √54 = 3√6
- 5√6 + 3√6 = 8√6
6.Simplify 5√6 × 5√6.
Answer: 150
- 5 × 5 = 25 and √6 × √6 = √36
- √36 = 6, so 25 × 6 = 150
7.Expand and simplify: √13(4 + √13)
Answer: 4√13 + 13
- √13 × 4 = 4√13
- √13 × √13 = 13
8.Rationalise the denominator:
Answer: 6√2
- Multiply top and bottom by √2:
- 12 ÷ 2 = 6, so 6√2
9.Simplify √50 − √32.
Answer: √2
- √50 = 5√2 and √32 = 4√2
- 5√2 − 4√2 = √2
10.Simplify 2√5 × 6√2.
Answer: 12√10
- 2 × 6 = 12 and √5 × √2 = √10
- 12√10
11.Expand and simplify: √15(7 + √15)
Answer: 7√15 + 15
- √15 × 7 = 7√15
- √15 × √15 = 15
12.Rationalise the denominator:
Answer: 4√15
- Multiply top and bottom by √15:
- 60 ÷ 15 = 4, so 4√15
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.