What this calculator does
A square root calculator answers the question that runs the other way from squaring: given a number, what value multiplied by itself produces it. The square root of 19, for example, is not a whole number, because 19 sits between the perfect squares 16 (4²) and 25 (5²), so its root sits between 4 and 5.
This calculator gives the principal (positive) square root of any non-negative number, notes both the positive and negative roots, and checks whether the number entered is a perfect square, one whose root is a whole number. If it is not, the nearest perfect squares below and above it are shown for context.
The formula
The principal square root of x is the non-negative number that, multiplied by itself, gives x. Every positive number actually has two square roots, a positive one and its negative mirror, since a negative number multiplied by itself also gives a positive result. Negative numbers have no real square root, because no real number squared is negative.
| Term | Meaning |
|---|---|
| √x | The principal (non-negative) square root of x. |
| Perfect square | A number whose square root is a whole number, such as 4, 9, 16 or 100. |
| Principal root | The positive square root, the one meant when √ is used without a ± sign. |
The inputs explained
| Field | What to enter |
|---|---|
| Number | The number to take the square root of. Must be zero or greater. |
When to use it
Solving x² = a for x
Whenever an equation reduces to x squared equals some number, the square root of that number gives the size of x, with the sign then decided by the context of the problem.
Checking whether a number is a perfect square
Spotting perfect squares quickly is useful in simplifying radicals and factoring quadratics; this calculator flags it directly rather than requiring a mental list of squares.
Working out a side length from an area
A square with a known area has a side length equal to the square root of that area, a common step in geometry and construction problems.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Square roots across a range of numbers, 13 square root and beyond
A mix of perfect squares and non-perfect squares, showing which numbers give a clean whole-number root.
| Number | √x (principal root) | Is it a perfect square? |
|---|---|---|
| 4 | 2.000 | Yes: 2² = 4 |
| 10 | 3.162 | No |
| 19 | 4.359 | No |
| 50 | 7.071 | No |
| 100 | 10.000 | Yes: 10² = 100 |
| 144 | 12.000 | Yes: 12² = 144 |
Questions
What is the square root of 19?
About 4.359. 19 is not a perfect square, since no whole number squared equals 19: it falls between 4² = 16 and 5² = 25.
Can a negative number have a square root?
Not a real one. Any real number squared is zero or positive, so there is no real number that squares to a negative result. Negative numbers do have roots in the complex number system, outside what this calculator covers.
What is the difference between a square root and a perfect square?
A perfect square is a whole number produced by squaring another whole number, such as 49 (7²). Its square root, 7, is itself a whole number. Most numbers are not perfect squares, and their square roots are irrational, non-repeating decimals.
How is the square root different from the cube root?
The square root asks what number squared (multiplied by itself twice) gives x; the cube root asks what number cubed (multiplied by itself three times) gives x. The exponents and roots calculator covers cube roots and any other root alongside powers.
To check any number against the full list of perfect squares nearby, see the perfect square calculator. For cube roots and other powers, see the exponents and roots calculator.