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 √125 + √80.
Answer: 9√5
- √125 = 5√5 and √80 = 4√5
- 5√5 + 4√5 = 9√5
2.Simplify 4√2 × 2√6.
Answer: 16√3
- 4 × 2 = 8 and √2 × √6 = √12
- √12 = 2√3, so 8 × 2√3 = 16√3
3.Expand and simplify: √7(1 + √7)
Answer: √7 + 7
- √7 × 1 = √7
- √7 × √7 = 7
4.Rationalise the denominator:
Answer: √3
- Multiply top and bottom by √3:
- 3 ÷ 3 = 1, so √3
5.Simplify √12 − √3.
Answer: √3
- √12 = 2√3 and √3 = √3
- 2√3 − √3 = √3
6.Simplify 6√2 × 6√3.
Answer: 36√6
- 6 × 6 = 36 and √2 × √3 = √6
- 36√6
7.Expand and simplify: √2(7 + √2)
Answer: 7√2 + 2
- √2 × 7 = 7√2
- √2 × √2 = 2
8.Rationalise the denominator:
Answer: 6√15
- Multiply top and bottom by √15:
- 90 ÷ 15 = 6, so 6√15
9.Simplify √32 + √50.
Answer: 9√2
- √32 = 4√2 and √50 = 5√2
- 4√2 + 5√2 = 9√2
10.Simplify 4√5 × 2√3.
Answer: 8√15
- 4 × 2 = 8 and √5 × √3 = √15
- 8√15
11.Expand and simplify: √11(1 + √11)
Answer: √11 + 11
- √11 × 1 = √11
- √11 × √11 = 11
12.Rationalise the denominator:
Answer: 6√2
- Multiply top and bottom by √2:
- 12 ÷ 2 = 6, so 6√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.