Square Root of 216 Simplified
Simplify Square Root Calculator
What is the square root of 216 simplified?
Answer
√216 = 6√6
216 = 36 × 6, and 36 = 6² is the largest perfect square that divides 216, so √216 = √36 × √6 = 6√6. Check: 6√6 ≈ 14.697, the same as √216 ≈ 14.697.
Simplifying √216 Step by Step
1. Prime factorization. — All Prime Factors of 216:
216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33
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 216 | Comes out of the root | Stays under the root |
|---|---|---|---|
| 2 | 3 | 2 | 2 |
| 3 | 3 | 3 | 3 |
3. Take the pairs out of the root.
√216 = √((2 × 2) × (3 × 3) × 2 × 3)
= 2 × 3 × √(2 × 3)
= 6√6
4. Check by squaring back.
6² × 6 = 36 × 6 = 216
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 216 simplified? (The answer is: 6√6). Enter a whole number (e.g. '216') and hit the 'Simplify' button.
Simplified Square Roots Table
| Number | Simplest radical form | Decimal value |
|---|---|---|
| 201 | √201 | ≈ 14.177 |
| 202 | √202 | ≈ 14.213 |
| 203 | √203 | ≈ 14.248 |
| 204 | 2√51 | ≈ 14.283 |
| 205 | √205 | ≈ 14.318 |
| 206 | √206 | ≈ 14.353 |
| 207 | 3√23 | ≈ 14.387 |
| 208 | 4√13 | ≈ 14.422 |
| 209 | √209 | ≈ 14.457 |
| 210 | √210 | ≈ 14.491 |
| 211 | √211 | ≈ 14.526 |
| 212 | 2√53 | ≈ 14.56 |
| 213 | √213 | ≈ 14.595 |
| 214 | √214 | ≈ 14.629 |
| 215 | √215 | ≈ 14.663 |
| 216 | 6√6 | ≈ 14.697 |
| 217 | √217 | ≈ 14.731 |
| 218 | √218 | ≈ 14.765 |
| 219 | √219 | ≈ 14.799 |
| 220 | 2√55 | ≈ 14.832 |
| 221 | √221 | ≈ 14.866 |
| 222 | √222 | ≈ 14.9 |
| 223 | √223 | ≈ 14.933 |
| 224 | 4√14 | ≈ 14.967 |
| 225 | 15 | 15 |
| 226 | √226 | ≈ 15.033 |
| 227 | √227 | ≈ 15.067 |
| 228 | 2√57 | ≈ 15.1 |
| 229 | √229 | ≈ 15.133 |
| 230 | √230 | ≈ 15.166 |
FAQ
What is the square root of 216 simplified?
√216 = 6√6
Is 216 a perfect square?
No. 216 = 36 × 6: its largest perfect square factor is 36 = 6², and the factor 6 stays under the radical, so √216 = 6√6.
What is √216 as a decimal?
√216 ≈ 14.697. The decimal never ends and never repeats, so it is always rounded; the exact value is 6√6.
What is the largest perfect square that divides 216?
36 = 6². Dividing gives 216 ÷ 36 = 6, and 6 has no square factor left, so √216 = √36 × √6 = 6√6.
See Also
- Square Root of 206 Simplified (already simplest)
- Square Root of 207 Simplified (3√23)
- Square Root of 208 Simplified (4√13)
- Square Root of 209 Simplified (already simplest)
- Square Root of 210 Simplified (already simplest)
- Square Root of 211 Simplified (already simplest)
- Square Root of 212 Simplified (2√53)
- Square Root of 213 Simplified (already simplest)
- Square Root of 214 Simplified (already simplest)
- Square Root of 215 Simplified (already simplest)
- Square Root of 217 Simplified (already simplest)
- Square Root of 218 Simplified (already simplest)
- Square Root of 219 Simplified (already simplest)
- Square Root of 220 Simplified (2√55)
- Square Root of 221 Simplified (already simplest)
- Square Root of 222 Simplified (already simplest)
- Square Root of 223 Simplified (already simplest)
- Square Root of 224 Simplified (4√14)
- Square Root of 225 Simplified (= 15)
- Square Root of 226 Simplified (already simplest)
- Вынести множитель из-под знака корня √216 (6√6)
- Simplificar la raíz cuadrada de 216 (6√6)
- Simplificar a raiz quadrada de 216 (6√6)