9th Grade Radicals Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √45 − √20.
Answer: √5
- √45 = 3√5 and √20 = 2√5
- 3√5 − 2√5 = √5
2.Simplify 3√3 × 5√15.
Answer: 45√5
- 3 × 5 = 15 and √3 × √15 = √45
- √45 = 3√5, so 15 × 3√5 = 45√5
3.Expand and simplify: √2(6 + √2)
Answer: 6√2 + 2
- √2 × 6 = 6√2
- √2 × √2 = 2
4.Rationalize the denominator:
Answer: 6√13
- Multiply top and bottom by √13:
- 78 ÷ 13 = 6, so 6√13
5.Simplify √48 + √3.
Answer: 5√3
- √48 = 4√3 and √3 = √3
- 4√3 + √3 = 5√3
6.Simplify 4√6 × 4√3.
Answer: 48√2
- 4 × 4 = 16 and √6 × √3 = √18
- √18 = 3√2, so 16 × 3√2 = 48√2
7.Expand and simplify: √3(3 + √3)
Answer: 3√3 + 3
- √3 × 3 = 3√3
- √3 × √3 = 3
8.Rationalize the denominator:
Answer: 5√10
- Multiply top and bottom by √10:
- 50 ÷ 10 = 5, so 5√10
9.Simplify √44 + √99.
Answer: 5√11
- √44 = 2√11 and √99 = 3√11
- 2√11 + 3√11 = 5√11
10.Simplify 5√5 × 6√6.
Answer: 30√30
- 5 × 6 = 30 and √5 × √6 = √30
- 30√30
11.Expand and simplify: √13(8 + √13)
Answer: 8√13 + 13
- √13 × 8 = 8√13
- √13 × √13 = 13
12.Rationalize the denominator:
Answer: 2√5
- Multiply top and bottom by √5:
- 10 ÷ 5 = 2, so 2√5
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.