Square Root of 772 Simplified
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What is the square root of 772 simplified?
Answer
√772 = 2√193
772 = 4 × 193, and 4 = 2² is the largest perfect square that divides 772, so √772 = √4 × √193 = 2√193. Check: 2√193 ≈ 27.785, the same as √772 ≈ 27.785.
Simplifying √772 Step by Step
1. Prime factorization. — All Prime Factors of 772:
772 = 2 × 2 × 193 = 22 × 193
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 772 | Comes out of the root | Stays under the root |
|---|---|---|---|
| 2 | 2 | 2 | — |
| 193 | 1 | — | 193 |
3. Take the pairs out of the root.
√772 = √((2 × 2) × 193)
= 2 × √193
= 2√193
4. Check by squaring back.
2² × 193 = 4 × 193 = 772
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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 |
|---|---|---|
| 495 | 3√55 | ≈ 22.249 |
| 500 | 10√5 | ≈ 22.361 |
| 507 | 13√3 | ≈ 22.517 |
| 514 | √514 | ≈ 22.672 |
| 525 | 5√21 | ≈ 22.913 |
| 528 | 4√33 | ≈ 22.978 |
| 550 | 5√22 | ≈ 23.452 |
| 600 | 10√6 | ≈ 24.495 |
| 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 |
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 772 simplified? (The answer is: 2√193). Enter a whole number (e.g. '772') and hit the 'Simplify' button.