Square Root of 1000 Simplified
Simplify Square Root Calculator
What is the square root of 1,000 simplified?
Answer
√1,000 = 10√10
1,000 = 100 × 10, and 100 = 10² is the largest perfect square that divides 1,000, so √1,000 = √100 × √10 = 10√10. Check: 10√10 ≈ 31.623, the same as √1,000 ≈ 31.623.
Simplifying √1,000 Step by Step
1. Prime factorization. — All Prime Factors of 1,000:
1,000 = 2 × 2 × 2 × 5 × 5 × 5 = 23 × 53
2. Pair up equal primes. Each pair is a perfect square and comes out of the root as one factor; a prime without a partner stays under the radical.
| Prime factor | Times in 1,000 | Comes out of the root | Stays under the root |
|---|---|---|---|
| 2 | 3 | 2 | 2 |
| 5 | 3 | 5 | 5 |
3. Take the pairs out of the root.
√1,000 = √((2 × 2) × (5 × 5) × 2 × 5)
= 2 × 5 × √(2 × 5)
= 10√10
4. Check by squaring back.
10² × 10 = 100 × 10 = 1,000
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See Also
- Square Root Calculator - Calculate the square root of any number
- Factors of a Number - List all Factors and Factor Pairs of a Number
- Prime Number Checker - Find out whether a given number is Prime or not
- Prime Factorization - Prime Factorization Calculator
- Prime Numbers List - List of all Prime Numbers - how many Prime numbers are between
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Simplified Square Roots Table
| Number | Simplest radical form | Decimal value |
|---|---|---|
| 675 | 15√3 | ≈ 25.981 |
| 720 | 12√5 | ≈ 26.833 |
| 725 | 5√29 | ≈ 26.926 |
| 726 | 11√6 | ≈ 26.944 |
| 729 | 27 | 27 |
| 750 | 5√30 | ≈ 27.386 |
| 756 | 6√21 | ≈ 27.495 |
| 772 | 2√193 | ≈ 27.785 |
| 780 | 2√195 | ≈ 27.928 |
| 800 | 20√2 | ≈ 28.284 |
| 850 | 5√34 | ≈ 29.155 |
| 875 | 5√35 | ≈ 29.58 |
| 880 | 4√55 | ≈ 29.665 |
| 960 | 8√15 | ≈ 30.984 |
| 972 | 18√3 | ≈ 31.177 |
| 1,000 | 10√10 | ≈ 31.623 |
| 1,200 | 20√3 | ≈ 34.641 |
| 1,250 | 25√2 | ≈ 35.355 |
| 1,260 | 6√35 | ≈ 35.496 |
| 1,280 | 16√5 | ≈ 35.777 |
| 1,296 | 36 | 36 |
| 1,575 | 15√7 | ≈ 39.686 |
| 1,875 | 25√3 | ≈ 43.301 |
| 2,000 | 20√5 | ≈ 44.721 |
| 2,016 | 12√14 | ≈ 44.9 |
| 3,780 | 6√105 | ≈ 61.482 |
| 5,000 | 50√2 | ≈ 70.711 |
| 7,200 | 60√2 | ≈ 84.853 |
| 8,000 | 40√5 | ≈ 89.443 |
| 12,500 | 50√5 | ≈ 111.803 |
Simplify Square Root Calculator
This calculator writes a square root in simplest radical form: it finds the largest perfect square that divides the number, takes its root out of the radical and leaves the rest under it. For example, it can help you find out what is the square root of 1,000 simplified? (The answer is: 10√10). Enter a whole number (e.g. '1,000') and hit the 'Simplify' button.