Square Root of 240 Simplified
Simplify Square Root Calculator
What is the square root of 240 simplified?
Answer
√240 = 4√15
240 = 16 × 15, and 16 = 4² is the largest perfect square that divides 240, so √240 = √16 × √15 = 4√15. Check: 4√15 ≈ 15.492, the same as √240 ≈ 15.492.
Simplifying √240 Step by Step
1. Prime factorization. — All Prime Factors of 240:
240 = 2 × 2 × 2 × 2 × 3 × 5 = 24 × 3 × 5
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 240 | Comes out of the root | Stays under the root |
|---|---|---|---|
| 2 | 4 | 22 | — |
| 3 | 1 | — | 3 |
| 5 | 1 | — | 5 |
3. Take the pairs out of the root.
√240 = √((2 × 2) × (2 × 2) × 3 × 5)
= 2 × 2 × √(3 × 5)
= 4√15
4. Check by squaring back.
4² × 15 = 16 × 15 = 240
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 240 simplified? (The answer is: 4√15). Enter a whole number (e.g. '240') and hit the 'Simplify' button.
Simplified Square Roots Table
| Number | Simplest radical form | Decimal value |
|---|---|---|
| 225 | 15 | 15 |
| 226 | √226 | ≈ 15.033 |
| 227 | √227 | ≈ 15.067 |
| 228 | 2√57 | ≈ 15.1 |
| 229 | √229 | ≈ 15.133 |
| 230 | √230 | ≈ 15.166 |
| 231 | √231 | ≈ 15.199 |
| 232 | 2√58 | ≈ 15.232 |
| 233 | √233 | ≈ 15.264 |
| 234 | 3√26 | ≈ 15.297 |
| 235 | √235 | ≈ 15.33 |
| 236 | 2√59 | ≈ 15.362 |
| 237 | √237 | ≈ 15.395 |
| 238 | √238 | ≈ 15.427 |
| 239 | √239 | ≈ 15.46 |
| 240 | 4√15 | ≈ 15.492 |
| 241 | √241 | ≈ 15.524 |
| 242 | 11√2 | ≈ 15.556 |
| 243 | 9√3 | ≈ 15.588 |
| 244 | 2√61 | ≈ 15.62 |
| 245 | 7√5 | ≈ 15.652 |
| 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 |
FAQ
What is the square root of 240 simplified?
√240 = 4√15
Is 240 a perfect square?
No. 240 = 16 × 15: its largest perfect square factor is 16 = 4², and the factor 15 stays under the radical, so √240 = 4√15.
What is √240 as a decimal?
√240 ≈ 15.492. The decimal never ends and never repeats, so it is always rounded; the exact value is 4√15.
What is the largest perfect square that divides 240?
16 = 4². Dividing gives 240 ÷ 16 = 15, and 15 has no square factor left, so √240 = √16 × √15 = 4√15.
See Also
- Square Root of 230 Simplified (already simplest)
- Square Root of 231 Simplified (already simplest)
- Square Root of 232 Simplified (2√58)
- Square Root of 233 Simplified (already simplest)
- Square Root of 234 Simplified (3√26)
- Square Root of 235 Simplified (already simplest)
- Square Root of 236 Simplified (2√59)
- Square Root of 237 Simplified (already simplest)
- Square Root of 238 Simplified (already simplest)
- Square Root of 239 Simplified (already simplest)
- Square Root of 241 Simplified (already simplest)
- Square Root of 242 Simplified (11√2)
- Square Root of 243 Simplified (9√3)
- Square Root of 244 Simplified (2√61)
- Square Root of 245 Simplified (7√5)
- Square Root of 246 Simplified (already simplest)
- Square Root of 247 Simplified (already simplest)
- Square Root of 248 Simplified (2√62)
- Square Root of 249 Simplified (already simplest)
- Square Root of 250 Simplified (5√10)
- Вынести множитель из-под знака корня √240 (4√15)
- Simplificar la raíz cuadrada de 240 (4√15)
- Simplificar a raiz quadrada de 240 (4√15)