10th Grade Radicals Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the 10th Grade exponents & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Indices & Scientific Notation10th Grade Radicals Worksheet — Level 2 — Practice Set 3 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √1134.
Answer: 9√14
- 1134 = 81 × 14
- √1134 = √81 × √14 = 9√14
2.Simplify 5√3 + 4√3.
Answer: 9√3
- These are like radicals (both √3)
- 5 + 4 = 9, so 9√3
3.Simplify √250 + √360.
Answer: 11√10
- √250 = 5√10 and √360 = 6√10
- 5√10 + 6√10 = 11√10
4.Simplify √40 × √160.
Answer: 80
- √40 × √160 = √6400
- = 80
5.Simplify √539.
Answer: 7√11
- 539 = 49 × 11
- √539 = √49 × √11 = 7√11
6.Simplify 8√11 + √11.
Answer: 9√11
- These are like radicals (both √11)
- 8 + 1 = 9, so 9√11
7.Simplify √250 + √40.
Answer: 7√10
- √250 = 5√10 and √40 = 2√10
- 5√10 + 2√10 = 7√10
8.Simplify √3 × √13.
Answer: √39
- √3 × √13 = √39
- 39 has no square factor, so √39 is simplest
9.Simplify √45.
Answer: 3√5
- 45 = 9 × 5
- √45 = √9 × √5 = 3√5
10.Simplify 7√15 − 6√15.
Answer: √15
- These are like radicals (both √15)
- 7 − 6 = 1, so √15
11.Simplify √28 + √63.
Answer: 5√7
- √28 = 2√7 and √63 = 3√7
- 2√7 + 3√7 = 5√7
12.Simplify √8 × √32.
Answer: 16
- √8 × √32 = √256
- √256 = 16
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.