10th Grade Radicals Worksheet — Level 2 — Practice Set 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 — 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 √567.
Answer: 9√7
- 567 = 81 × 7
- √567 = √81 × √7 = 9√7
2.Simplify 3√15 + 2√15.
Answer: 5√15
- These are like radicals (both √15)
- 3 + 2 = 5, so 5√15
3.Simplify √28 + √175.
Answer: 7√7
- √28 = 2√7 and √175 = 5√7
- 2√7 + 5√7 = 7√7
4.Simplify √20 × √80.
Answer: 40
- √20 × √80 = √1600
- √1600 = 40
5.Simplify √468.
Answer: 6√13
- 468 = 36 × 13
- √468 = √36 × √13 = 6√13
6.Simplify 2√11 − √11.
Answer: √11
- These are like radicals (both √11)
- 2 − 1 = 1, so √11
7.Simplify √3 + √12.
Answer: 3√3
- √3 = √3 and √12 = 2√3
- √3 + 2√3 = 3√3
8.Simplify √5 × √7.
Answer: √35
- √5 × √7 = √35
- 35 has no square factor, so √35 is simplest
9.Simplify √54.
Answer: 3√6
- 54 = 9 × 6
- √54 = √9 × √6 = 3√6
10.Simplify 7√15 + 3√15.
Answer: 10√15
- These are like radicals (both √15)
- 7 + 3 = 10, so 10√15
11.Simplify √20 + √5.
Answer: 3√5
- √20 = 2√5 and √5 = √5
- 2√5 + √5 = 3√5
12.Simplify √7 × √28.
Answer: 14
- √7 × √28 = √196
- = 14
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.