Year 10 Surds Worksheet — Level 2 — 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 2 — 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 √96.
Answer: 4√6
- 96 = 16 × 6
- √96 = √16 × √6 = 4√6
2.Simplify 6√14 − 5√14.
Answer: √14
- These are like surds (both √14)
- 6 − 5 = 1, so √14
3.Simplify √208 + √13.
Answer: 5√13
- √208 = 4√13 and √13 = √13
- 4√13 + √13 = 5√13
4.Simplify √56 × √126.
Answer: 84
- √56 × √126 = √7056
- √7056 = 84
5.Simplify √75.
Answer: 5√3
- 75 = 25 × 3
- √75 = √25 × √3 = 5√3
6.Simplify 9√2 − 5√2.
Answer: 4√2
- These are like surds (both √2)
- 9 − 5 = 4, so 4√2
7.Simplify √224 + √126.
Answer: 7√14
- √224 = 4√14 and √126 = 3√14
- 4√14 + 3√14 = 7√14
8.Simplify √2 × √13.
Answer: √26
- √2 × √13 = √26
- 26 has no square factor, so √26 is simplest
9.Simplify √54.
Answer: 3√6
- 54 = 9 × 6
- √54 = √9 × √6 = 3√6
10.Simplify 6√10 + 2√10.
Answer: 8√10
- These are like surds (both √10)
- 6 + 2 = 8, so 8√10
11.Simplify √12 + √3.
Answer: 3√3
- √12 = 2√3 and √3 = √3
- 2√3 + √3 = 3√3
12.Simplify √3 × √13.
Answer: √39
- √3 × √13 = √39
- 39 has no square factor, so √39 is simplest
Marking tips
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