10th Grade Radicals Worksheet — Level 3 — 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 3 — 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 √208 − √117.
Answer: √13
- √208 = 4√13 and √117 = 3√13
- 4√13 − 3√13 = √13
2.Simplify 5√3 × 5√6.
Answer: 75√2
- 5 × 5 = 25 and √3 × √6 = √18
- √18 = 3√2, so 25 × 3√2 = 75√2
3.Expand and simplify: √6(5 + √6)
Answer: 5√6 + 6
- √6 × 5 = 5√6
- √6 × √6 = 6
4.Rationalize the denominator:
Answer: 3√15
- Multiply top and bottom by √15:
- 45 ÷ 15 = 3, so 3√15
5.Simplify √45 − √20.
Answer: √5
- √45 = 3√5 and √20 = 2√5
- 3√5 − 2√5 = √5
6.Simplify 2√6 × 4√10.
Answer: 16√15
- 2 × 4 = 8 and √6 × √10 = √60
- √60 = 2√15, so 8 × 2√15 = 16√15
7.Expand and simplify: √3(1 + √3)
Answer: √3 + 3
- √3 × 1 = √3
- √3 × √3 = 3
8.Rationalize the denominator:
Answer: 6√14
- Multiply top and bottom by √14:
- 84 ÷ 14 = 6, so 6√14
9.Simplify √275 − √99.
Answer: 2√11
- √275 = 5√11 and √99 = 3√11
- 5√11 − 3√11 = 2√11
10.Simplify 2√2 × 6√3.
Answer: 12√6
- 2 × 6 = 12 and √2 × √3 = √6
- 12√6
11.Expand and simplify: √10(8 + √10)
Answer: 8√10 + 10
- √10 × 8 = 8√10
- √10 × √10 = 10
12.Rationalize the denominator:
Answer: 3√3
- Multiply top and bottom by √3:
- 9 ÷ 3 = 3, so 3√3
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.