10th Grade Radicals Worksheet — Level 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 3 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √28 + √7.
Answer: 3√7
- √28 = 2√7 and √7 = √7
- 2√7 + √7 = 3√7
2.Simplify 4√2 × 6√10.
Answer: 48√5
- 4 × 6 = 24 and √2 × √10 = √20
- √20 = 2√5, so 24 × 2√5 = 48√5
3.Expand and simplify: √5(5 + √5)
Answer: 5√5 + 5
- √5 × 5 = 5√5
- √5 × √5 = 5
4.Rationalize the denominator:
Answer: 6√2
- Multiply top and bottom by √2:
- 12 ÷ 2 = 6, so 6√2
5.Simplify √27 − √12.
Answer: √3
- √27 = 3√3 and √12 = 2√3
- 3√3 − 2√3 = √3
6.Simplify 4√2 × 2√3.
Answer: 8√6
- 4 × 2 = 8 and √2 × √3 = √6
- 8√6
7.Expand and simplify: √2(3 + √2)
Answer: 3√2 + 2
- √2 × 3 = 3√2
- √2 × √2 = 2
8.Rationalize the denominator:
Answer: 2√3
- Multiply top and bottom by √3:
- 6 ÷ 3 = 2, so 2√3
9.Simplify √44 + √99.
Answer: 5√11
- √44 = 2√11 and √99 = 3√11
- 2√11 + 3√11 = 5√11
10.Simplify 3√3 × 4√2.
Answer: 12√6
- 3 × 4 = 12 and √3 × √2 = √6
- 12√6
11.Expand and simplify: √15(8 + √15)
Answer: 8√15 + 15
- √15 × 8 = 8√15
- √15 × √15 = 15
12.Rationalize the denominator:
Answer: 2√14
- Multiply top and bottom by √14:
- 28 ÷ 14 = 2, so 2√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.