Instantly find the square root (√) of any number with our free Square Root Calculator. Get quick, accurate results with perfect square checks and step-by-step solutions.
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Perfect Square Examples – Click to Try:
Calculation Result
DEMO
Square Root
12
√144 = 12
Perfect Square ✓
Original Number
144
Positive Root (+√)
+12
Negative Root (-√)
-12
| Property | Value |
|---|---|
| Original Number | 144 |
| Principal Square Root | 12 |
| Positive Root (+√) | +12 |
| Negative Root (-√) | -12 |
| Verification | 12² = 12 × 12 = 144 ✓ |
| Exponent Form | 144^(1/2) = 12 |
| Decimal Precision | 12.000000 |
| Prime Factorization | 2 × 2 × 2 × 2 × 3 × 3 |
Square Root Formula:
√x = y where y² = x (y × y = x)
Example: √144 = 12, because 12 × 12 = 144
Note: Every positive number has two square roots: positive and negative
Perfect Square: A number whose square root is an integer (e.g., 4, 9, 16, 25…)
For negative numbers: √(-x) results in imaginary numbers (complex roots)
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