Year 10 Surds Worksheet — Level 3 — 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 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √208 + √325.
Answer: 9√13
- √208 = 4√13 and √325 = 5√13
- 4√13 + 5√13 = 9√13
2.Simplify 3√6 × 4√2.
Answer: 24√3
- 3 × 4 = 12 and √6 × √2 = √12
- √12 = 2√3, so 12 × 2√3 = 24√3
3.Expand and simplify: √3(7 + √3)
Answer: 7√3 + 3
- √3 × 7 = 7√3
- √3 × √3 = 3
4.Rationalise the denominator:
Answer: 2√5
- Multiply top and bottom by √5:
- 10 ÷ 5 = 2, so 2√5
5.Simplify √40 − √10.
Answer: √10
- √40 = 2√10 and √10 = √10
- 2√10 − √10 = √10
6.Simplify 3√2 × 3√3.
Answer: 9√6
- 3 × 3 = 9 and √2 × √3 = √6
- 9√6
7.Expand and simplify: √7(2 + √7)
Answer: 2√7 + 7
- √7 × 2 = 2√7
- √7 × √7 = 7
8.Rationalise the denominator:
Answer: 4√7
- Multiply top and bottom by √7:
- 28 ÷ 7 = 4, so 4√7
9.Simplify √44 − √11.
Answer: √11
- √44 = 2√11 and √11 = √11
- 2√11 − √11 = √11
10.Simplify 5√6 × 6√3.
Answer: 90√2
- 5 × 6 = 30 and √6 × √3 = √18
- √18 = 3√2, so 30 × 3√2 = 90√2
11.Expand and simplify: √10(8 + √10)
Answer: 8√10 + 10
- √10 × 8 = 8√10
- √10 × √10 = 10
12.Rationalise the denominator:
Answer: 4√14
- Multiply top and bottom by √14:
- 56 ÷ 14 = 4, so 4√14
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.