9th Grade Radicals Worksheet — Level 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 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √240 − √15.
Answer: 3√15
- √240 = 4√15 and √15 = √15
- 4√15 − √15 = 3√15
2.Simplify 2√6 × 2√15.
Answer: 12√10
- 2 × 2 = 4 and √6 × √15 = √90
- √90 = 3√10, so 4 × 3√10 = 12√10
3.Expand and simplify: √3(3 + √3)
Answer: 3√3 + 3
- √3 × 3 = 3√3
- √3 × √3 = 3
4.Rationalize the denominator:
Answer: √14
- Multiply top and bottom by √14:
- 14 ÷ 14 = 1, so √14
5.Simplify √150 − √96.
Answer: √6
- √150 = 5√6 and √96 = 4√6
- 5√6 − 4√6 = √6
6.Simplify 5√2 × 6√15.
Answer: 30√30
- 5 × 6 = 30 and √2 × √15 = √30
- 30√30
7.Expand and simplify: √7(8 + √7)
Answer: 8√7 + 7
- √7 × 8 = 8√7
- √7 × √7 = 7
8.Rationalize the denominator:
Answer: 6√14
- Multiply top and bottom by √14:
- 84 ÷ 14 = 6, so 6√14
9.Simplify √40 + √90.
Answer: 5√10
- √40 = 2√10 and √90 = 3√10
- 2√10 + 3√10 = 5√10
10.Simplify 4√2 × 5√6.
Answer: 40√3
- 4 × 5 = 20 and √2 × √6 = √12
- √12 = 2√3, so 20 × 2√3 = 40√3
11.Expand and simplify: √6(6 + √6)
Answer: 6√6 + 6
- √6 × 6 = 6√6
- √6 × √6 = 6
12.Rationalize the denominator:
Answer: 5√2
- Multiply top and bottom by √2:
- 10 ÷ 2 = 5, so 5√2
Marking tips
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