9th Grade Radicals Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 9th Grade exponents & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheet9th Grade · Mathematics · Indices & Scientific Notation9th Grade Radicals Worksheet — Level 2 — Practice Set 2 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √686.
Answer: 7√14
- 686 = 49 × 14
- √686 = √49 × √14 = 7√14
2.Simplify 3√10 + 8√10.
Answer: 11√10
- These are like radicals (both √10)
- 3 + 8 = 11, so 11√10
3.Simplify √14 + √56.
Answer: 3√14
- √14 = √14 and √56 = 2√14
- √14 + 2√14 = 3√14
4.Simplify √11 × √44.
Answer: 22
- √11 × √44 = √484
- = 22
5.Simplify √200.
Answer: 10√2
- 200 = 100 × 2
- √200 = √100 × √2 = 10√2
6.Simplify 4√14 + 4√14.
Answer: 8√14
- These are like radicals (both √14)
- 4 + 4 = 8, so 8√14
7.Simplify √7 + √28.
Answer: 3√7
- √7 = √7 and √28 = 2√7
- √7 + 2√7 = 3√7
8.Simplify √2 × √13.
Answer: √26
- √2 × √13 = √26
- 26 has no square factor, so √26 is simplest
9.Simplify √540.
Answer: 6√15
- 540 = 36 × 15
- √540 = √36 × √15 = 6√15
10.Simplify 2√7 + 2√7.
Answer: 4√7
- These are like radicals (both √7)
- 2 + 2 = 4, so 4√7
11.Simplify √80 + √5.
Answer: 5√5
- √80 = 4√5 and √5 = √5
- 4√5 + √5 = 5√5
12.Simplify √45 × √20.
Answer: 30
- √45 × √20 = √900
- √900 = 30
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.