Year 11 Surds Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 11 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Indices & Scientific NotationYear 11 Surds Worksheet — Level 3 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √90 + √160.
Answer: 7√10
- √90 = 3√10 and √160 = 4√10
- 3√10 + 4√10 = 7√10
2.Simplify 4√5 × 5√15.
Answer: 100√3
- 4 × 5 = 20 and √5 × √15 = √75
- √75 = 5√3, so 20 × 5√3 = 100√3
3.Expand and simplify: √5(1 + √5)
Answer: √5 + 5
- √5 × 1 = √5
- √5 × √5 = 5
4.Rationalise the denominator:
Answer: 3√7
- Multiply top and bottom by √7:
- 21 ÷ 7 = 3, so 3√7
5.Simplify √125 − √20.
Answer: 3√5
- √125 = 5√5 and √20 = 2√5
- 5√5 − 2√5 = 3√5
6.Simplify 5√2 × 2√10.
Answer: 20√5
- 5 × 2 = 10 and √2 × √10 = √20
- √20 = 2√5, so 10 × 2√5 = 20√5
7.Expand and simplify: √2(4 + √2)
Answer: 4√2 + 2
- √2 × 4 = 4√2
- √2 × √2 = 2
8.Rationalise the denominator:
Answer: 6√10
- Multiply top and bottom by √10:
- 60 ÷ 10 = 6, so 6√10
9.Simplify √375 − √60.
Answer: 3√15
- √375 = 5√15 and √60 = 2√15
- 5√15 − 2√15 = 3√15
10.Simplify 3√6 × 2√10.
Answer: 12√15
- 3 × 2 = 6 and √6 × √10 = √60
- √60 = 2√15, so 6 × 2√15 = 12√15
11.Expand and simplify: √11(2 + √11)
Answer: 2√11 + 11
- √11 × 2 = 2√11
- √11 × √11 = 11
12.Rationalise the denominator:
Answer: 4√11
- Multiply top and bottom by √11:
- 44 ÷ 11 = 4, so 4√11
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.