Square Root Calculator
Formula
√n = n^(1/2)
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √144 = 12 because 12 × 12 = 144.
How to use
- Type a non-negative value into the Number field.
- The tool calculates the square root instantly.
- Read the Square Root result, shown to six decimals.
Example
Enter 144 and the result is √144 = 12, because 12 × 12 = 144. The square root tells you the side length of a square with that area.
Frequently Asked Questions
What is a perfect square?
A perfect square is a number whose square root is a whole number. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
Can you take the square root of a negative number?
Not in the real number system. The square root of a negative number involves imaginary numbers (e.g., √-1 = i). This calculator works with non-negative numbers only.
What is the square root of 2?
√2 ≈ 1.414214. It's an irrational number, meaning it has infinite non-repeating decimal places.
How do you estimate a square root without a calculator?
Find the two perfect squares the number falls between and interpolate. For example, 50 sits between 49 (square root 7) and 64 (square root 8), and since 50 is just above 49, the answer is close to 7.07. This estimation method gets you within a few percent and is useful for quick mental checks.
What is the difference between a square root and a cube root?
A square root asks what number multiplied by itself gives the original value, while a cube root asks what number multiplied by itself three times does. For example, the square root of 64 is 8 (8 x 8), but the cube root of 64 is 4 (4 x 4 x 4). Square roots are written with the radical symbol, and cube roots add a small 3 in the notch of the radical.