Year 10 Surds Worksheet — Level 3 — Practice Set 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 — Practice Set 3 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √18 − √2.
Answer: 2√2
- √18 = 3√2 and √2 = √2
- 3√2 − √2 = 2√2
2.Simplify 3√5 × 2√15.
Answer: 30√3
- 3 × 2 = 6 and √5 × √15 = √75
- √75 = 5√3, so 6 × 5√3 = 30√3
3.Expand and simplify: √2(9 + √2)
Answer: 9√2 + 2
- √2 × 9 = 9√2
- √2 × √2 = 2
4.Rationalise the denominator:
Answer: √11
- Multiply top and bottom by √11:
- 11 ÷ 11 = 1, so √11
5.Simplify √135 + √375.
Answer: 8√15
- √135 = 3√15 and √375 = 5√15
- 3√15 + 5√15 = 8√15
6.Simplify 4√2 × 3√6.
Answer: 24√3
- 4 × 3 = 12 and √2 × √6 = √12
- √12 = 2√3, so 12 × 2√3 = 24√3
7.Expand and simplify: √6(5 + √6)
Answer: 5√6 + 6
- √6 × 5 = 5√6
- √6 × √6 = 6
8.Rationalise the denominator:
Answer: 2√6
- Multiply top and bottom by √6:
- 12 ÷ 6 = 2, so 2√6
9.Simplify √52 + √325.
Answer: 7√13
- √52 = 2√13 and √325 = 5√13
- 2√13 + 5√13 = 7√13
10.Simplify 3√6 × 5√6.
Answer: 90
- 3 × 5 = 15 and √6 × √6 = √36
- √36 = 6, so 15 × 6 = 90
11.Expand and simplify: √15(9 + √15)
Answer: 9√15 + 15
- √15 × 9 = 9√15
- √15 × √15 = 15
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.