Square Root of 4000
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What is the square root of 4,000?
Answer
√4,000 ≈ 63.2455532034
√4,000 = 20√10
√4,000 is irrational: its decimals never end and never repeat — rounded to 10 decimal places. √ is the non-negative root; x² = 4,000 also has −√4,000 ≈ −63.2455532034.
√4,000 ≈ 63.2455532034
3,969 = 63²4,096 = 64²
- Between squares
- 63² = 3,969 < 4,000 < 4,096 = 64², so 63 < √4,000 < 64
- Simplified
- 4,000 = 20² × 10, so √4,000 = 20√10
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Square Root Table
| Number | Square Root | Perfect Square |
|---|---|---|
| 2,401 | 49 | Yes |
| 2,500 | 50 | Yes |
| 2,601 | 51 | Yes |
| 2,704 | 52 | Yes |
| 2,809 | 53 | Yes |
| 2,916 | 54 | Yes |
| 3,000 | 54.7722557505 | No |
| 3,025 | 55 | Yes |
| 3,136 | 56 | Yes |
| 3,249 | 57 | Yes |
| 3,364 | 58 | Yes |
| 3,600 | 60 | Yes |
| 3,721 | 61 | Yes |
| 3,844 | 62 | Yes |
| 3,969 | 63 | Yes |
| 4,000 | 63.2455532034 | No |
| 4,096 | 64 | Yes |
| 4,225 | 65 | Yes |
| 4,356 | 66 | Yes |
| 4,489 | 67 | Yes |
| 4,624 | 68 | Yes |
| 4,761 | 69 | Yes |
| 4,900 | 70 | Yes |
| 5,000 | 70.7106781187 | No |
| 5,041 | 71 | Yes |
| 5,184 | 72 | Yes |
| 5,329 | 73 | Yes |
| 5,476 | 74 | Yes |
| 5,625 | 75 | Yes |
| 5,776 | 76 | Yes |