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 √72.
Answer: 6√2
- 72 = 36 × 2
- √72 = √36 × √2 = 6√2
2.Simplify 3√11 + 5√11.
Answer: 8√11
- These are like surds (both √11)
- 3 + 5 = 8, so 8√11
3.Simplify √2 + √50.
Answer: 6√2
- √2 = √2 and √50 = 5√2
- √2 + 5√2 = 6√2
4.Simplify √2 × √13.
Answer: √26
- √2 × √13 = √26
- 26 has no square factor, so √26 is simplest
5.Simplify √56.
Answer: 2√14
- 56 = 4 × 14
- √56 = √4 × √14 = 2√14
6.Simplify 4√3 − 2√3.
Answer: 2√3
- These are like surds (both √3)
- 4 − 2 = 2, so 2√3
7.Simplify √375 + √240.
Answer: 9√15
- √375 = 5√15 and √240 = 4√15
- 5√15 + 4√15 = 9√15
8.Simplify √8 × √32.
Answer: 16
- √8 × √32 = √256
- √256 = 16
9.Simplify √1400.
Answer: 10√14
- 1400 = 100 × 14
- √1400 = √100 × √14 = 10√14
10.Simplify 9√15 + √15.
Answer: 10√15
- These are like surds (both √15)
- 9 + 1 = 10, so 10√15
11.Simplify √126 + √224.
Answer: 7√14
- √126 = 3√14 and √224 = 4√14
- 3√14 + 4√14 = 7√14
12.Simplify √3 × √11.
Answer: √33
- √3 × √11 = √33
- 33 has no square factor, so √33 is simplest
Marking tips
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