10th Grade Radicals Worksheet — Level 2 — 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 2 — 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 √1500.
Answer: 10√15
- 1500 = 100 × 15
- √1500 = √100 × √15 = 10√15
2.Simplify 9√14 − 8√14.
Answer: √14
- These are like radicals (both √14)
- 9 − 8 = 1, so √14
3.Simplify √275 + √99.
Answer: 8√11
- √275 = 5√11 and √99 = 3√11
- 5√11 + 3√11 = 8√11
4.Simplify √5 × √45.
Answer: 15
- √5 × √45 = √225
- √225 = 15
5.Simplify √375.
Answer: 5√15
- 375 = 25 × 15
- √375 = √25 × √15 = 5√15
6.Simplify 4√3 + 8√3.
Answer: 12√3
- These are like radicals (both √3)
- 4 + 8 = 12, so 12√3
7.Simplify √112 + √175.
Answer: 9√7
- √112 = 4√7 and √175 = 5√7
- 4√7 + 5√7 = 9√7
8.Simplify √3 × √7.
Answer: √21
- √3 × √7 = √21
- 21 has no square factor, so √21 is simplest
9.Simplify √180.
Answer: 6√5
- 180 = 36 × 5
- √180 = √36 × √5 = 6√5
10.Simplify 2√3 + 7√3.
Answer: 9√3
- These are like radicals (both √3)
- 2 + 7 = 9, so 9√3
11.Simplify √7 + √63.
Answer: 4√7
- √7 = √7 and √63 = 3√7
- √7 + 3√7 = 4√7
12.Simplify √2 × √13.
Answer: √26
- √2 × √13 = √26
- 26 has no square factor, so √26 is simplest
Marking tips
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