How to Use
- Enter a number
Type the number whose root you want to calculate.
- Select root index
Choose square root (2), cube root (3), or enter a custom root index.
- View result
Click Calculate to see the approximate value and simplified radical form.
What is a square root?
A square root is the value that, when multiplied by itself, produces the original number. For a number x, the value r that satisfies r² = x is the square root of x, written with the √ symbol. For example, the square root of 16 is 4, because multiplying 4 by itself gives 16.
A square root is the inverse of raising a number to a power. Beyond the square root (√), it generalizes to the nth root for any index n, such as the cube root (∛) or the fourth root (∜). Numbers that are the square of an integer, like 4, 9, and 16, are called perfect squares, and their square roots come out to exact integers.
Square roots are widely used to recover lengths and magnitudes, such as finding the hypotenuse with the Pythagorean theorem, computing the distance between two points, calculating standard deviation, or working with physical speed formulas.
Formula
The nth root is defined as a power with the exponent 1/n.
nth root(x) = x^(1/n)
Here, x is the number under the radical and n is the index (2 for a square root, 3 for a cube root). For example, √72 equals 72^(1/2) ≈ 8.485281. Simplified, since 72 = 36 × 2, we get √72 = √36 × √2 = 6√2.
This calculator rounds the result to an integer and raises it back to the nth power; if it matches the original value closely (error below 1e-9), it shows the exact value, otherwise it shows an approximate value to 10 decimal places.