pääkvadraattijuuri

Pääkvadraattijuuri, also known as the principal square root, refers to the non-negative square root of a number. When a number has two square roots, one positive and one negative, the principal square root is the positive one. For example, the number 9 has two square roots: 3 and -3. The principal square root of 9 is 3. This convention is widely adopted in mathematics to ensure a unique value for the square root operation.

The symbol for the principal square root is the radical sign, $\sqrt{}$. So, $\sqrt{9} = 3$. If the intention is to refer to both square roots, the $\pm$ symbol is used, as in $\pm \sqrt{9} = \pm 3$. The concept of the principal square root is particularly important in areas like algebra and calculus where functions are involved. For instance, the function $f(x) = \sqrt{x}$ is defined to return only the principal square root.

In the context of real numbers, only non-negative numbers have real principal square roots. The principal square root of 0 is 0. For positive real numbers, the principal square root is always a positive real number. When dealing with complex numbers, the concept of principal square root is extended, but typically still refers to the root with a non-negative real part, or if the real part is zero, the root with a non-negative imaginary part.