Year 11 Surds Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Indices & Scientific NotationYear 11 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 √72 − √50.
Answer: √2
- √72 = 6√2 and √50 = 5√2
- 6√2 − 5√2 = √2
2.Simplify 6√5 × 6√15.
Answer: 180√3
- 6 × 6 = 36 and √5 × √15 = √75
- √75 = 5√3, so 36 × 5√3 = 180√3
3.Expand and simplify: √15(1 + √15)
Answer: √15 + 15
- √15 × 1 = √15
- √15 × √15 = 15
4.Rationalise the denominator:
Answer: 4√6
- Multiply top and bottom by √6:
- 24 ÷ 6 = 4, so 4√6
5.Simplify √40 + √160.
Answer: 6√10
- √40 = 2√10 and √160 = 4√10
- 2√10 + 4√10 = 6√10
6.Simplify 6√5 × 3√10.
Answer: 90√2
- 6 × 3 = 18 and √5 × √10 = √50
- √50 = 5√2, so 18 × 5√2 = 90√2
7.Expand and simplify: √11(3 + √11)
Answer: 3√11 + 11
- √11 × 3 = 3√11
- √11 × √11 = 11
8.Rationalise the denominator:
Answer: 6√15
- Multiply top and bottom by √15:
- 90 ÷ 15 = 6, so 6√15
9.Simplify √18 − √8.
Answer: √2
- √18 = 3√2 and √8 = 2√2
- 3√2 − 2√2 = √2
10.Simplify 4√2 × 4√6.
Answer: 32√3
- 4 × 4 = 16 and √2 × √6 = √12
- √12 = 2√3, so 16 × 2√3 = 32√3
11.Expand and simplify: √11(8 + √11)
Answer: 8√11 + 11
- √11 × 8 = 8√11
- √11 × √11 = 11
12.Rationalise the denominator:
Answer: 6√14
- Multiply top and bottom by √14:
- 84 ÷ 14 = 6, so 6√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.