Year 9 Surds Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 9 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Indices & Scientific NotationYear 9 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 √75 − √48.
Answer: √3
- √75 = 5√3 and √48 = 4√3
- 5√3 − 4√3 = √3
2.Simplify 2√3 × 4√3.
Answer: 24
- 2 × 4 = 8 and √3 × √3 = √9
- √9 = 3, so 8 × 3 = 24
3.Expand and simplify: √13(7 + √13)
Answer: 7√13 + 13
- √13 × 7 = 7√13
- √13 × √13 = 13
4.Rationalise the denominator:
Answer: 4√3
- Multiply top and bottom by √3:
- 12 ÷ 3 = 4, so 4√3
5.Simplify √54 − √24.
Answer: √6
- √54 = 3√6 and √24 = 2√6
- 3√6 − 2√6 = √6
6.Simplify 6√3 × 5√15.
Answer: 90√5
- 6 × 5 = 30 and √3 × √15 = √45
- √45 = 3√5, so 30 × 3√5 = 90√5
7.Expand and simplify: √11(8 + √11)
Answer: 8√11 + 11
- √11 × 8 = 8√11
- √11 × √11 = 11
8.Rationalise the denominator:
Answer: 4√7
- Multiply top and bottom by √7:
- 28 ÷ 7 = 4, so 4√7
9.Simplify √3 + √12.
Answer: 3√3
- √3 = √3 and √12 = 2√3
- √3 + 2√3 = 3√3
10.Simplify 4√2 × 3√15.
Answer: 12√30
- 4 × 3 = 12 and √2 × √15 = √30
- 12√30
11.Expand and simplify: √15(8 + √15)
Answer: 8√15 + 15
- √15 × 8 = 8√15
- √15 × √15 = 15
12.Rationalise the denominator:
Answer: √10
- Multiply top and bottom by √10:
- 10 ÷ 10 = 1, so √10
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.