Let's simplify each of the square roots step by step. The goal is to
factor out perfect squares from under the square root and simplify.
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11) √28
Factor 28:
28 = 4 × 7
√28 = √(4 × 7) = √4 × √7 = 2√7
✔ Answer: 2√7
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12) √45
Factor 45:
45 = 9 × 5
√45 = √(9 × 5) = √9 × √5 = 3√5
✔ Answer: 3√5
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13) √98
Factor 98:
98 = 49 × 2
√98 = √(49 × 2) = √49 × √2 = 7√2
✔ Answer: 7√2
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14) √24
Factor 24:
24 = 4 × 6
√24 = √(4 × 6) = √4 × √6 = 2√6
✔ Answer: 2√6
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15) √300
Factor 300:
300 = 100 × 3
√300 = √(100 × 3) = √100 × √3 = 10√3
✔ Answer: 10√3
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16) √44
Factor 44:
44 = 4 × 11
√44 = √(4 × 11) = √4 × √11 = 2√11
✔ Answer: 2√11
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17) √90
Factor 90:
90 = 9 × 10
√90 = √(9 × 10) = √9 × √10 = 3√10
✔ Answer: 3√10
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18) √48
Factor 48:
48 = 16 × 3
√48 = √(16 × 3) = √16 × √3 = 4√3
✔ Answer: 4√3
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✔ Final Answers:
| Problem | Simplified Form |
|--------|-----------------|
| 11) √28 | 2√7 |
| 12) √45 | 3√5 |
| 13) √98 | 7√2 |
| 14) √24 | 2√6 |
| 15) √300 | 10√3 |
| 16) √44 | 2√11 |
| 17) √90 | 3√10 |
| 18) √48 | 4√3 |
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🔍 Summary of Strategy:
To simplify a square root:
1. Find the
largest perfect square that divides the number.
2. Write the number as a product of that perfect square and another number.
3. Take the square root of the perfect square outside the radical.
4. Leave the other factor inside the square root.
This method works for all square root simplification problems!
Parent Tip: Review the logic above to help your child master the concept of simplifying square roots worksheet answers.
