Square Root of 252 Simplified
Simplify Square Root Calculator
What is the square root of 252 simplified?
Answer
√252 = 6√7
252 = 36 × 7, and 36 = 6² is the largest perfect square that divides 252, so √252 = √36 × √7 = 6√7. Check: 6√7 ≈ 15.875, the same as √252 ≈ 15.875.
Simplifying √252 Step by Step
1. Prime factorization. — All Prime Factors of 252:
252 = 2 × 2 × 3 × 3 × 7 = 22 × 32 × 7
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 252 | Comes out of the root | Stays under the root |
|---|---|---|---|
| 2 | 2 | 2 | — |
| 3 | 2 | 3 | — |
| 7 | 1 | — | 7 |
3. Take the pairs out of the root.
√252 = √((2 × 2) × (3 × 3) × 7)
= 2 × 3 × √7
= 6√7
4. Check by squaring back.
6² × 7 = 36 × 7 = 252
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 252 simplified? (The answer is: 6√7). Enter a whole number (e.g. '252') and hit the 'Simplify' button.
Simplified Square Roots Table
| Number | Simplest radical form | Decimal value |
|---|---|---|
| 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 |
| 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 |
FAQ
What is the square root of 252 simplified?
√252 = 6√7
Is 252 a perfect square?
No. 252 = 36 × 7: its largest perfect square factor is 36 = 6², and the factor 7 stays under the radical, so √252 = 6√7.
What is √252 as a decimal?
√252 ≈ 15.875. The decimal never ends and never repeats, so it is always rounded; the exact value is 6√7.
What is the largest perfect square that divides 252?
36 = 6². Dividing gives 252 ÷ 36 = 7, and 7 has no square factor left, so √252 = √36 × √7 = 6√7.
See Also
- 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)
- Square Root of 251 Simplified (already simplest)
- 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 261 Simplified (3√29)
- Square Root of 262 Simplified (already simplest)
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