Square Root of 5000 Simplified
Simplify Square Root Calculator
What is the square root of 5,000 simplified?
Answer
√5,000 = 50√2
5,000 = 2,500 × 2, and 2,500 = 50² is the largest perfect square that divides 5,000, so √5,000 = √2,500 × √2 = 50√2. Check: 50√2 ≈ 70.711, the same as √5,000 ≈ 70.711.
Simplifying √5,000 Step by Step
1. Prime factorization. — All Prime Factors of 5,000:
5,000 = 2 × 2 × 2 × 5 × 5 × 5 × 5 = 23 × 54
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 5,000 | Comes out of the root | Stays under the root |
|---|---|---|---|
| 2 | 3 | 2 | 2 |
| 5 | 4 | 52 | — |
3. Take the pairs out of the root.
√5,000 = √((2 × 2) × (5 × 5) × (5 × 5) × 2)
= 2 × 5 × 5 × √2
= 50√2
4. Check by squaring back.
50² × 2 = 2,500 × 2 = 5,000
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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
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 5,000 simplified? (The answer is: 50√2). Enter a whole number (e.g. '5,000') and hit the 'Simplify' button.
Simplified Square Roots Table
| Number | Simplest radical form | Decimal value |
|---|---|---|
| 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 |
| 20,000 | 100√2 | ≈ 141.421 |
| 84,500 | 130√5 | ≈ 290.689 |
FAQ
What is the square root of 5,000 simplified?
√5,000 = 50√2
Is 5,000 a perfect square?
No. 5,000 = 2,500 × 2: its largest perfect square factor is 2,500 = 50², and the factor 2 stays under the radical, so √5,000 = 50√2.
What is √5,000 as a decimal?
√5,000 ≈ 70.711. The decimal never ends and never repeats, so it is always rounded; the exact value is 50√2.
What is the largest perfect square that divides 5,000?
2,500 = 50². Dividing gives 5,000 ÷ 2,500 = 2, and 2 has no square factor left, so √5,000 = √2,500 × √2 = 50√2.
See Also
- Square Root of 1200 Simplified (20√3)
- Square Root of 1250 Simplified (25√2)
- Square Root of 1260 Simplified (6√35)
- Square Root of 1280 Simplified (16√5)
- Square Root of 1296 Simplified (= 36)
- Square Root of 1575 Simplified (15√7)
- Square Root of 1875 Simplified (25√3)
- Square Root of 2000 Simplified (20√5)
- Square Root of 2016 Simplified (12√14)
- Square Root of 3780 Simplified (6√105)
- Square Root of 7200 Simplified (60√2)
- Square Root of 8000 Simplified (40√5)
- Square Root of 12500 Simplified (50√5)
- Square Root of 20000 Simplified (100√2)
- Square Root of 84500 Simplified (130√5)
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