Calculator inputs
Formula used
Principal square root: √n = n1/2
Equation roots: x² = n gives x = ±√n
Negative input: √(−n) = i√n
Nth root: ⁿ√a = a1/n
A square root reverses the operation of squaring. The principal root is normally non-negative. Equations may require both positive and negative roots.
How to use
- Select the calculation mode.
- Enter a number, fraction, or supported expression.
- Choose precision, rounding, and result options.
- Press Calculate to view exact and decimal results.
- Copy, export, print, or review saved history.
Example data
| Input | Exact form | Decimal value | Classification |
|---|---|---|---|
| 81 | 9 | 9 | Perfect square |
| 72 | 6√2 | 8.48528137 | Irrational root |
| 2/3 | √6/3 | 0.81649658 | Fractional radical |
| -25 | 5i | 5i | Pure imaginary root |
Calculation history
No calculations are stored in this session yet.
Frequently asked questions
What is a principal square root?
It is the non-negative square root of a number. For example, the principal square root of nine is three. Equation solving may still require both possible signed roots.
Why does x² = 9 have two answers?
Both three and negative three square to nine. Therefore, the equation has two real solutions. The radical symbol alone usually means the principal root.
Can this calculator simplify radicals?
Yes, it extracts perfect-square factors from integer radicands. For example, it changes √72 into 6√2. Very large integers may remain unsimplified for performance safety.
Does it accept fractions?
Yes, simple fractions and division expressions are supported. Exact fractional roots are reduced when practical. A zero denominator always produces a clear error.
Can negative numbers have square roots?
Negative numbers have no real square roots. They do have roots involving the imaginary unit i. Enable complex mode to display those results correctly.
What expressions can I enter?
You may use arithmetic, powers, parentheses, and scientific notation. Constants pi and e are also supported. Selected functions include abs, sqrt, sin, cos, and log.
How is rounding handled?
You can choose nearest, down, up, or truncation. Precision ranges from zero through fifteen decimal places. Exact radical forms remain independent from decimal rounding.
What is a perfect square?
A perfect square is an integer squared exactly. Examples include zero, one, four, nine, and sixteen. Their principal square roots are whole non-negative numbers.
Can I generate a square-root table?
Yes, choose the perfect-squares table mode. Enter an integer start and ending value. The calculator generates up to five hundred one rows.