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 √50 − √32.
Answer: √2
- √50 = 5√2 and √32 = 4√2
- 5√2 − 4√2 = √2
2.Simplify 5√2 × 2√6.
Answer: 20√3
- 5 × 2 = 10 and √2 × √6 = √12
- √12 = 2√3, so 10 × 2√3 = 20√3
3.Expand and simplify: √14(7 + √14)
Answer: 7√14 + 14
- √14 × 7 = 7√14
- √14 × √14 = 14
4.Rationalise the denominator:
Answer: 3√6
- Multiply top and bottom by √6:
- 18 ÷ 6 = 3, so 3√6
5.Simplify √375 − √240.
Answer: √15
- √375 = 5√15 and √240 = 4√15
- 5√15 − 4√15 = √15
6.Simplify 6√3 × 6√15.
Answer: 108√5
- 6 × 6 = 36 and √3 × √15 = √45
- √45 = 3√5, so 36 × 3√5 = 108√5
7.Expand and simplify: √7(8 + √7)
Answer: 8√7 + 7
- √7 × 8 = 8√7
- √7 × √7 = 7
8.Rationalise the denominator:
Answer: 5√2
- Multiply top and bottom by √2:
- 10 ÷ 2 = 5, so 5√2
9.Simplify √44 + √275.
Answer: 7√11
- √44 = 2√11 and √275 = 5√11
- 2√11 + 5√11 = 7√11
10.Simplify 5√5 × 4√15.
Answer: 100√3
- 5 × 4 = 20 and √5 × √15 = √75
- √75 = 5√3, so 20 × 5√3 = 100√3
11.Expand and simplify: √13(7 + √13)
Answer: 7√13 + 13
- √13 × 7 = 7√13
- √13 × √13 = 13
12.Rationalise the denominator:
Answer: 6√3
- Multiply top and bottom by √3:
- 18 ÷ 3 = 6, so 6√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.
- Celebrate what went well first, then pick one thing to work on next.