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 √48 + √75.
Answer: 9√3
- √48 = 4√3 and √75 = 5√3
- 4√3 + 5√3 = 9√3
2.Simplify 5√3 × 2√15.
Answer: 30√5
- 5 × 2 = 10 and √3 × √15 = √45
- √45 = 3√5, so 10 × 3√5 = 30√5
3.Expand and simplify: √13(4 + √13)
Answer: 4√13 + 13
- √13 × 4 = 4√13
- √13 × √13 = 13
4.Rationalise the denominator:
Answer: 6√7
- Multiply top and bottom by √7:
- 42 ÷ 7 = 6, so 6√7
5.Simplify √99 + √275.
Answer: 8√11
- √99 = 3√11 and √275 = 5√11
- 3√11 + 5√11 = 8√11
6.Simplify 3√5 × 3√6.
Answer: 9√30
- 3 × 3 = 9 and √5 × √6 = √30
- 9√30
7.Expand and simplify: √14(6 + √14)
Answer: 6√14 + 14
- √14 × 6 = 6√14
- √14 × √14 = 14
8.Rationalise the denominator:
Answer: 4√15
- Multiply top and bottom by √15:
- 60 ÷ 15 = 4, so 4√15
9.Simplify √20 − √5.
Answer: √5
- √20 = 2√5 and √5 = √5
- 2√5 − √5 = √5
10.Simplify 6√5 × 3√6.
Answer: 18√30
- 6 × 3 = 18 and √5 × √6 = √30
- 18√30
11.Expand and simplify: √11(2 + √11)
Answer: 2√11 + 11
- √11 × 2 = 2√11
- √11 × √11 = 11
12.Rationalise the denominator:
Answer: √14
- Multiply top and bottom by √14:
- 14 ÷ 14 = 1, so √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.