How to use the Square Root Calculator
Enter any number zero or above. You get the square root as a decimal and, when it simplifies, in radical form such as 6√2.
Perfect squares and simplifying
A perfect square like 144 has a whole number root, 12. Other numbers can often be simplified by pulling out the biggest perfect square factor: 72 is 36 × 2, so √72 = 6√2, about 8.4853. Simplified forms are exact, which is why maths classes prefer them to rounded decimals.
Square roots in everyday problems
Square roots turn areas into lengths. A square room of 20 m² has sides of √20, about 4.47 m. They also give diagonals: a square with 1 m sides has a diagonal of √2, about 1.414 m. Negative numbers have no real square root, so the calculator only accepts zero and above.
The formula
√n
Examples
- Square root of 72
√72 = 8.48528137 Simplified: 6√2
- Square root of 144
√144 = 12 Perfect square: 12 × 12
- Square root of 2
√2 = 1.41421356 Already in simplest radical form.
Limitations and assumptions
Computed in your browser with standard double-precision arithmetic unless the page says otherwise. Very large or very small values may be rounded.
Frequently asked questions
What is a perfect square?
A whole number whose square root is also a whole number, such as 49 or 144.
How do I simplify a square root?
Pull out the largest perfect-square factor: √72 = √(36 × 2) = 6√2.
Can you take the square root of a negative number?
Not within the real numbers; the result is imaginary.
How do I calculate other roots?
Use the exponent calculator with a fractional power, such as 1/3 for a cube root.