Year 10 Surds Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √11 + √99.
Answer: 4√11
- √11 = √11 and √99 = 3√11
- √11 + 3√11 = 4√11
2.Simplify 4√3 × 6√6.
Answer: 72√2
- 4 × 6 = 24 and √3 × √6 = √18
- √18 = 3√2, so 24 × 3√2 = 72√2
3.Expand and simplify: √6(2 + √6)
Answer: 2√6 + 6
- √6 × 2 = 2√6
- √6 × √6 = 6
4.Rationalise the denominator:
Answer: 4√10
- Multiply top and bottom by √10:
- 40 ÷ 10 = 4, so 4√10
5.Simplify √80 + √5.
Answer: 5√5
- √80 = 4√5 and √5 = √5
- 4√5 + √5 = 5√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: √10(3 + √10)
Answer: 3√10 + 10
- √10 × 3 = 3√10
- √10 × √10 = 10
8.Rationalise the denominator:
Answer: 2√10
- Multiply top and bottom by √10:
- 20 ÷ 10 = 2, so 2√10
9.Simplify √20 − √5.
Answer: √5
- √20 = 2√5 and √5 = √5
- 2√5 − √5 = √5
10.Simplify 3√6 × 5√10.
Answer: 30√15
- 3 × 5 = 15 and √6 × √10 = √60
- √60 = 2√15, so 15 × 2√15 = 30√15
11.Expand and simplify: √3(1 + √3)
Answer: √3 + 3
- √3 × 1 = √3
- √3 × √3 = 3
12.Rationalise the denominator:
Answer: 3√5
- Multiply top and bottom by √5:
- 15 ÷ 5 = 3, so 3√5
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.