10th Grade Radicals Worksheet — Level 3 — 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 3 — 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 √375 − √135.
Answer: 2√15
- √375 = 5√15 and √135 = 3√15
- 5√15 − 3√15 = 2√15
2.Simplify 5√3 × 4√2.
Answer: 20√6
- 5 × 4 = 20 and √3 × √2 = √6
- 20√6
3.Expand and simplify: √11(7 + √11)
Answer: 7√11 + 11
- √11 × 7 = 7√11
- √11 × √11 = 11
4.Rationalize the denominator:
Answer: 4√7
- Multiply top and bottom by √7:
- 28 ÷ 7 = 4, so 4√7
5.Simplify √112 − √63.
Answer: √7
- √112 = 4√7 and √63 = 3√7
- 4√7 − 3√7 = √7
6.Simplify 5√3 × 2√15.
Answer: 30√5
- 5 × 2 = 10 and √3 × √15 = √45
- √45 = 3√5, so 10 × 3√5 = 30√5
7.Expand and simplify: √5(2 + √5)
Answer: 2√5 + 5
- √5 × 2 = 2√5
- √5 × √5 = 5
8.Rationalize the denominator:
Answer: 2√10
- Multiply top and bottom by √10:
- 20 ÷ 10 = 2, so 2√10
9.Simplify √44 + √99.
Answer: 5√11
- √44 = 2√11 and √99 = 3√11
- 2√11 + 3√11 = 5√11
10.Simplify 6√5 × 3√3.
Answer: 18√15
- 6 × 3 = 18 and √5 × √3 = √15
- 18√15
11.Expand and simplify: √5(8 + √5)
Answer: 8√5 + 5
- √5 × 8 = 8√5
- √5 × √5 = 5
12.Rationalize the denominator:
Answer: √11
- Multiply top and bottom by √11:
- 11 ÷ 11 = 1, so √11
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.