9th Grade Radicals Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √18 − √2.
Answer: 2√2
- √18 = 3√2 and √2 = √2
- 3√2 − √2 = 2√2
2.Simplify 3√2 × 4√6.
Answer: 24√3
- 3 × 4 = 12 and √2 × √6 = √12
- √12 = 2√3, so 12 × 2√3 = 24√3
3.Expand and simplify: √3(7 + √3)
Answer: 7√3 + 3
- √3 × 7 = 7√3
- √3 × √3 = 3
4.Rationalize the denominator:
Answer: 2√5
- Multiply top and bottom by √5:
- 10 ÷ 5 = 2, so 2√5
5.Simplify √11 + √275.
Answer: 6√11
- √11 = √11 and √275 = 5√11
- √11 + 5√11 = 6√11
6.Simplify 6√5 × 3√6.
Answer: 18√30
- 6 × 3 = 18 and √5 × √6 = √30
- 18√30
7.Expand and simplify: √5(1 + √5)
Answer: √5 + 5
- √5 × 1 = √5
- √5 × √5 = 5
8.Rationalize the denominator:
Answer: 6√7
- Multiply top and bottom by √7:
- 42 ÷ 7 = 6, so 6√7
9.Simplify √224 − √126.
Answer: √14
- √224 = 4√14 and √126 = 3√14
- 4√14 − 3√14 = √14
10.Simplify 2√2 × 5√15.
Answer: 10√30
- 2 × 5 = 10 and √2 × √15 = √30
- 10√30
11.Expand and simplify: √14(9 + √14)
Answer: 9√14 + 14
- √14 × 9 = 9√14
- √14 × √14 = 14
12.Rationalize the denominator:
Answer: 4√5
- Multiply top and bottom by √5:
- 20 ÷ 5 = 4, so 4√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.
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