Enter a non-negative number to find its principal square root. The calculator also shows the negative solution to the equation x² = a.
Square Root Calculator
How to use the calculator
- Enter a non-negative integer or decimal.
- Select Calculate. The principal root and the negative solution to x² = a will appear.
- Select Clear to start again.
What is a square root?
The principal square root of a non-negative number a is the non-negative value x such that x² = a. It is written √a. For example, √25 = 5 because 5² = 25.
The symbol √a means the principal, non-negative root. However, when solving x² = a with a > 0, there are two solutions: x = √a and x = −√a.
Square root formula
A square root is also a power with exponent one half:
√a = a1/2
Square root examples
| Number (a) | Principal root (√a) | Negative solution (−√a) |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | −1 |
| 4 | 2 | −2 |
| 9 | 3 | −3 |
| 16 | 4 | −4 |
| 25 | 5 | −5 |
| 2 | ≈ 1.41421 | ≈ −1.41421 |
| 3 | ≈ 1.73205 | ≈ −1.73205 |
Frequently asked questions about square roots
What is a square root?
The principal square root of a is the non-negative number x such that x² = a. For example, √25 = 5.
Does a negative number have a square root?
Not in the real numbers. Square roots of negative numbers can be represented using complex numbers.
What is the square root of 2?
It is approximately 1.41421356. It is irrational, so its decimal expansion neither ends nor repeats.
What is a perfect square?
A perfect square is an integer obtained by squaring another integer, such as 1, 4, 9, 16, 25, 36, 49, 64, 81, or 100.
Why does the calculator show two values?
√a is the principal non-negative root. The second value is shown because the equation x² = a has both a positive and a negative solution when a is positive.
See also…
