Square Root Calculator Formula & How It Works
√n = n^(1/2) | ∛n = n^(1/3) | ⁿ√x = x^(1/n)
- Square root: the number that when squared gives n
- √9 = 3 because 3² = 9
- Negative numbers have no real square root (imaginary: √-1 = i)
- nth root: x^(1/n), or equivalently x^0.5 for square root
The square root of a number n is the value that when multiplied by itself gives n. Perfect squares (1, 4, 9, 16, 25…) have whole-number square roots. Others are irrational: √2 = 1.41421… For cube roots and higher, the same logic applies with the appropriate exponent.