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 √240 − √15.
Answer: 3√15
- √240 = 4√15 and √15 = √15
- 4√15 − √15 = 3√15
2.Simplify 3√6 × 3√15.
Answer: 27√10
- 3 × 3 = 9 and √6 × √15 = √90
- √90 = 3√10, so 9 × 3√10 = 27√10
3.Expand and simplify: √6(4 + √6)
Answer: 4√6 + 6
- √6 × 4 = 4√6
- √6 × √6 = 6
4.Rationalise the denominator:
Answer: √6
- Multiply top and bottom by √6:
- 6 ÷ 6 = 1, so √6
5.Simplify √99 + √176.
Answer: 7√11
- √99 = 3√11 and √176 = 4√11
- 3√11 + 4√11 = 7√11
6.Simplify 4√2 × 5√3.
Answer: 20√6
- 4 × 5 = 20 and √2 × √3 = √6
- 20√6
7.Expand and simplify: √3(5 + √3)
Answer: 5√3 + 3
- √3 × 5 = 5√3
- √3 × √3 = 3
8.Rationalise the denominator:
Answer: √5
- Multiply top and bottom by √5:
- 5 ÷ 5 = 1, so √5
9.Simplify √3 + √12.
Answer: 3√3
- √3 = √3 and √12 = 2√3
- √3 + 2√3 = 3√3
10.Simplify 4√5 × 4√15.
Answer: 80√3
- 4 × 4 = 16 and √5 × √15 = √75
- √75 = 5√3, so 16 × 5√3 = 80√3
11.Expand and simplify: √13(4 + √13)
Answer: 4√13 + 13
- √13 × 4 = 4√13
- √13 × √13 = 13
12.Rationalise the denominator:
Answer: 5√11
- Multiply top and bottom by √11:
- 55 ÷ 11 = 5, so 5√11
Marking tips
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