9th Grade Radicals Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the 9th Grade exponents & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheet9th Grade · Mathematics · Indices & Scientific Notation9th 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 √150 − √6.
Answer: 4√6
- √150 = 5√6 and √6 = √6
- 5√6 − √6 = 4√6
2.Simplify 5√2 × 2√2.
Answer: 20
- 5 × 2 = 10 and √2 × √2 = √4
- √4 = 2, so 10 × 2 = 20
3.Expand and simplify: √7(4 + √7)
Answer: 4√7 + 7
- √7 × 4 = 4√7
- √7 × √7 = 7
4.Rationalize the denominator:
Answer: √14
- Multiply top and bottom by √14:
- 14 ÷ 14 = 1, so √14
5.Simplify √60 + √135.
Answer: 5√15
- √60 = 2√15 and √135 = 3√15
- 2√15 + 3√15 = 5√15
6.Simplify 6√3 × 6√15.
Answer: 108√5
- 6 × 6 = 36 and √3 × √15 = √45
- √45 = 3√5, so 36 × 3√5 = 108√5
7.Expand and simplify: √3(4 + √3)
Answer: 4√3 + 3
- √3 × 4 = 4√3
- √3 × √3 = 3
8.Rationalize the denominator:
Answer: √2
- Multiply top and bottom by √2:
- 2 ÷ 2 = 1, so √2
9.Simplify √90 + √160.
Answer: 7√10
- √90 = 3√10 and √160 = 4√10
- 3√10 + 4√10 = 7√10
10.Simplify 5√5 × 5√10.
Answer: 125√2
- 5 × 5 = 25 and √5 × √10 = √50
- √50 = 5√2, so 25 × 5√2 = 125√2
11.Expand and simplify: √5(7 + √5)
Answer: 7√5 + 5
- √5 × 7 = 7√5
- √5 × √5 = 5
12.Rationalize the denominator:
Answer: 4√6
- Multiply top and bottom by √6:
- 24 ÷ 6 = 4, so 4√6
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.