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 √3 + √75.
Answer: 6√3
- √3 = √3 and √75 = 5√3
- √3 + 5√3 = 6√3
2.Simplify 3√2 × 5√10.
Answer: 30√5
- 3 × 5 = 15 and √2 × √10 = √20
- √20 = 2√5, so 15 × 2√5 = 30√5
3.Expand and simplify: √5(6 + √5)
Answer: 6√5 + 5
- √5 × 6 = 6√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 √175 + √112.
Answer: 9√7
- √175 = 5√7 and √112 = 4√7
- 5√7 + 4√7 = 9√7
6.Simplify 4√3 × 6√15.
Answer: 72√5
- 4 × 6 = 24 and √3 × √15 = √45
- √45 = 3√5, so 24 × 3√5 = 72√5
7.Expand and simplify: √10(1 + √10)
Answer: √10 + 10
- √10 × 1 = √10
- √10 × √10 = 10
8.Rationalise the denominator:
Answer: 3√15
- Multiply top and bottom by √15:
- 45 ÷ 15 = 3, so 3√15
9.Simplify √375 − √135.
Answer: 2√15
- √375 = 5√15 and √135 = 3√15
- 5√15 − 3√15 = 2√15
10.Simplify 4√3 × 4√15.
Answer: 48√5
- 4 × 4 = 16 and √3 × √15 = √45
- √45 = 3√5, so 16 × 3√5 = 48√5
11.Expand and simplify: √15(5 + √15)
Answer: 5√15 + 15
- √15 × 5 = 5√15
- √15 × √15 = 15
12.Rationalise the denominator:
Answer: 4√3
- Multiply top and bottom by √3:
- 12 ÷ 3 = 4, so 4√3
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.