Year 9 Surds Worksheet — Level 2 — 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 2 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √54.
Answer: 3√6
- 54 = 9 × 6
- √54 = √9 × √6 = 3√6
2.Simplify 8√7 + 8√7.
Answer: 16√7
- These are like surds (both √7)
- 8 + 8 = 16, so 16√7
3.Simplify √112 + √175.
Answer: 9√7
- √112 = 4√7 and √175 = 5√7
- 4√7 + 5√7 = 9√7
4.Simplify √6 × √96.
Answer: 24
- √6 × √96 = √576
- √576 = 24
5.Simplify √896.
Answer: 8√14
- 896 = 64 × 14
- √896 = √64 × √14 = 8√14
6.Simplify 4√5 + 7√5.
Answer: 11√5
- These are like surds (both √5)
- 4 + 7 = 11, so 11√5
7.Simplify √12 + √75.
Answer: 7√3
- √12 = 2√3 and √75 = 5√3
- 2√3 + 5√3 = 7√3
8.Simplify √52 × √208.
Answer: 104
- √52 × √208 = √10816
- √10816 = 104
9.Simplify √75.
Answer: 5√3
- 75 = 25 × 3
- √75 = √25 × √3 = 5√3
10.Simplify 4√11 − 3√11.
Answer: √11
- These are like surds (both √11)
- 4 − 3 = 1, so √11
11.Simplify √6 + √96.
Answer: 5√6
- √6 = √6 and √96 = 4√6
- √6 + 4√6 = 5√6
12.Simplify √3 × √11.
Answer: √33
- √3 × √11 = √33
- 33 has no square factor, so √33 is simplest
Marking tips
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