10th Grade Radicals Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √275 − √44.
Answer: 3√11
- √275 = 5√11 and √44 = 2√11
- 5√11 − 2√11 = 3√11
2.Simplify 2√6 × 2√3.
Answer: 12√2
- 2 × 2 = 4 and √6 × √3 = √18
- √18 = 3√2, so 4 × 3√2 = 12√2
3.Expand and simplify: √6(9 + √6)
Answer: 9√6 + 6
- √6 × 9 = 9√6
- √6 × √6 = 6
4.Rationalize the denominator:
Answer: 2√15
- Multiply top and bottom by √15:
- 30 ÷ 15 = 2, so 2√15
5.Simplify √150 − √6.
Answer: 4√6
- √150 = 5√6 and √6 = √6
- 5√6 − √6 = 4√6
6.Simplify 5√5 × 6√3.
Answer: 30√15
- 5 × 6 = 30 and √5 × √3 = √15
- 30√15
7.Expand and simplify: √5(1 + √5)
Answer: √5 + 5
- √5 × 1 = √5
- √5 × √5 = 5
8.Rationalize the denominator:
Answer: 4√14
- Multiply top and bottom by √14:
- 56 ÷ 14 = 4, so 4√14
9.Simplify √80 + √20.
Answer: 6√5
- √80 = 4√5 and √20 = 2√5
- 4√5 + 2√5 = 6√5
10.Simplify 5√3 × 3√15.
Answer: 45√5
- 5 × 3 = 15 and √3 × √15 = √45
- √45 = 3√5, so 15 × 3√5 = 45√5
11.Expand and simplify: √3(5 + √3)
Answer: 5√3 + 3
- √3 × 5 = 5√3
- √3 × √3 = 3
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.