Square Root of 261 Simplified
Simplify Square Root Calculator
What is the square root of 261 simplified?
Answer
√261 = 3√29
261 = 9 × 29, and 9 = 3² is the largest perfect square that divides 261, so √261 = √9 × √29 = 3√29. Check: 3√29 ≈ 16.155, the same as √261 ≈ 16.155.
Simplifying √261 Step by Step
1. Prime factorization. — All Prime Factors of 261:
261 = 3 × 3 × 29 = 32 × 29
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 261 | Comes out of the root | Stays under the root |
|---|---|---|---|
| 3 | 2 | 3 | — |
| 29 | 1 | — | 29 |
3. Take the pairs out of the root.
√261 = √((3 × 3) × 29)
= 3 × √29
= 3√29
4. Check by squaring back.
3² × 29 = 9 × 29 = 261
Related Calculations
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 261 simplified? (The answer is: 3√29). Enter a whole number (e.g. '261') and hit the 'Simplify' button.
Simplified Square Roots Table
| Number | Simplest radical form | Decimal value |
|---|---|---|
| 246 | √246 | ≈ 15.684 |
| 247 | √247 | ≈ 15.716 |
| 248 | 2√62 | ≈ 15.748 |
| 249 | √249 | ≈ 15.78 |
| 250 | 5√10 | ≈ 15.811 |
| 251 | √251 | ≈ 15.843 |
| 252 | 6√7 | ≈ 15.875 |
| 253 | √253 | ≈ 15.906 |
| 254 | √254 | ≈ 15.937 |
| 255 | √255 | ≈ 15.969 |
| 256 | 16 | 16 |
| 257 | √257 | ≈ 16.031 |
| 258 | √258 | ≈ 16.062 |
| 259 | √259 | ≈ 16.093 |
| 260 | 2√65 | ≈ 16.125 |
| 261 | 3√29 | ≈ 16.155 |
| 262 | √262 | ≈ 16.186 |
| 263 | √263 | ≈ 16.217 |
| 264 | 2√66 | ≈ 16.248 |
| 265 | √265 | ≈ 16.279 |
| 266 | √266 | ≈ 16.31 |
| 267 | √267 | ≈ 16.34 |
| 268 | 2√67 | ≈ 16.371 |
| 269 | √269 | ≈ 16.401 |
| 270 | 3√30 | ≈ 16.432 |
| 271 | √271 | ≈ 16.462 |
| 272 | 4√17 | ≈ 16.492 |
| 273 | √273 | ≈ 16.523 |
| 274 | √274 | ≈ 16.553 |
| 275 | 5√11 | ≈ 16.583 |
FAQ
What is the square root of 261 simplified?
√261 = 3√29
Is 261 a perfect square?
No. 261 = 9 × 29: its largest perfect square factor is 9 = 3², and the factor 29 stays under the radical, so √261 = 3√29.
What is √261 as a decimal?
√261 ≈ 16.155. The decimal never ends and never repeats, so it is always rounded; the exact value is 3√29.
What is the largest perfect square that divides 261?
9 = 3². Dividing gives 261 ÷ 9 = 29, and 29 has no square factor left, so √261 = √9 × √29 = 3√29.
See Also
- Square Root of 251 Simplified (already simplest)
- Square Root of 252 Simplified (6√7)
- Square Root of 253 Simplified (already simplest)
- Square Root of 254 Simplified (already simplest)
- Square Root of 255 Simplified (already simplest)
- Square Root of 256 Simplified (= 16)
- Square Root of 257 Simplified (already simplest)
- Square Root of 258 Simplified (already simplest)
- Square Root of 259 Simplified (already simplest)
- Square Root of 260 Simplified (2√65)
- Square Root of 262 Simplified (already simplest)
- Square Root of 263 Simplified (already simplest)
- Square Root of 264 Simplified (2√66)
- Square Root of 265 Simplified (already simplest)
- Square Root of 266 Simplified (already simplest)
- Square Root of 267 Simplified (already simplest)
- Square Root of 268 Simplified (2√67)
- Square Root of 269 Simplified (already simplest)
- Square Root of 270 Simplified (3√30)
- Square Root of 271 Simplified (already simplest)
- Вынести множитель из-под знака корня √261 (3√29)
- Simplificar la raíz cuadrada de 261 (3√29)
- Simplificar a raiz quadrada de 261 (3√29)