Instant Real-Time Calculation
Square Root Calculator
Calculate real and complex square roots instantly with step-by-step breakdowns, simplified radical form, and prime factorization.
Quick Inputs
How Square Root Calculation Works
1
Perfect Squares
Numbers whose square roots are whole integers (e.g., √16 = 4, √144 = 12).
2
Irrational Roots
Non-perfect squares result in non-repeating decimals (e.g., √2 ≈ 1.414213).
3
Negative Roots
Roots of negative numbers yield imaginary unit values (i), where i = √-1.
First 15 Perfect Squares Reference
| Number ($n$) | Square ($n^2$) | Square Root ($\sqrt{n^2}$) |
|---|---|---|
| 1 | 1 | √1 = 1 |
| 2 | 4 | √4 = 2 |
| 3 | 9 | √9 = 3 |
| 4 | 16 | √16 = 4 |
| 5 | 25 | √25 = 5 |
| 6 | 36 | √36 = 6 |
| 7 | 49 | √49 = 7 |
| 8 | 64 | √64 = 8 |
| 9 | 81 | √81 = 9 |
| 10 | 100 | √100 = 10 |
| 11 | 121 | √121 = 11 |
| 12 | 144 | √144 = 12 |
| 13 | 169 | √169 = 13 |
| 14 | 196 | √196 = 14 |
| 15 | 225 | √225 = 15 |