10th Grade Radicals Worksheet — Level 2 — 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 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √640.
Answer: 8√10
- 640 = 64 × 10
- √640 = √64 × √10 = 8√10
2.Simplify 3√15 + 4√15.
Answer: 7√15
- These are like radicals (both √15)
- 3 + 4 = 7, so 7√15
3.Simplify √11 + √44.
Answer: 3√11
- √11 = √11 and √44 = 2√11
- √11 + 2√11 = 3√11
4.Simplify √2 × √11.
Answer: √22
- √2 × √11 = √22
- 22 has no square factor, so √22 is simplest
5.Simplify √45.
Answer: 3√5
- 45 = 9 × 5
- √45 = √9 × √5 = 3√5
6.Simplify 7√10 + 9√10.
Answer: 16√10
- These are like radicals (both √10)
- 7 + 9 = 16, so 16√10
7.Simplify √117 + √208.
Answer: 7√13
- √117 = 3√13 and √208 = 4√13
- 3√13 + 4√13 = 7√13
8.Simplify √8 × √18.
Answer: 12
- √8 × √18 = √144
- √144 = 12
9.Simplify √98.
Answer: 7√2
- 98 = 49 × 2
- √98 = √49 × √2 = 7√2
10.Simplify 8√11 − 6√11.
Answer: 2√11
- These are like radicals (both √11)
- 8 − 6 = 2, so 2√11
11.Simplify √224 + √14.
Answer: 5√14
- √224 = 4√14 and √14 = √14
- 4√14 + √14 = 5√14
12.Simplify √126 × √56.
Answer: 84
- √126 × √56 = √7056
- √7056 = 84
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.