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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1. √8
Factor 8:
8 = 4 × 2
√8 = √(4 × 2) = √4 × √2 = 2√2
✔ Answer: 2√2
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2. √45
Factor 45:
45 = 9 × 5
√45 = √(9 × 5) = √9 × √5 = 3√5
✔ Answer: 3√5
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3. √18
Factor 18:
18 = 9 × 2
√18 = √(9 × 2) = √9 × √2 = 3√2
✔ Answer: 3√2
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4. √32
Factor 32:
32 = 16 × 2
√32 = √(16 × 2) = √16 × √2 = 4√2
✔ Answer: 4√2
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5. √27
Factor 27:
27 = 9 × 3
√27 = √(9 × 3) = √9 × √3 = 3√3
✔ Answer: 3√3
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6. √49
49 is a perfect square:
√49 = 7
✔ Answer: 7
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7. √28
Factor 28:
28 = 4 × 7
√28 = √(4 × 7) = √4 × √7 = 2√7
✔ Answer: 2√7
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8. √128
Factor 128:
128 = 64 × 2
√128 = √(64 × 2) = √64 × √2 = 8√2
✔ Answer: 8√2
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9. √75
Factor 75:
75 = 25 × 3
√75 = √(25 × 3) = √25 × √3 = 5√3
✔ Answer: 5√3
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10. √96
Factor 96:
96 = 16 × 6
√96 = √(16 × 6) = √16 × √6 = 4√6
✔ Answer: 4√6
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✔ Final Answers:
| Original | Simplified |
|--------|------------|
| √8 | 2√2 |
| √45 | 3√5 |
| √18 | 3√2 |
| √32 | 4√2 |
| √27 | 3√3 |
| √49 | 7 |
| √28 | 2√7 |
| √128 | 8√2 |
| √75 | 5√3 |
| √96 | 4√6 |
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💡
Tip: Always look for the largest
perfect square factor of the number under the radical. Then use the property:
> √(a × b) = √a × √b
This helps simplify square roots efficiently.
Let me know if you'd like a printable version or explanation with diagrams!
Parent Tip: Review the logic above to help your child master the concept of square and square root worksheet.
