Principal Square Root and Notation

Property The principal square root is the positive square root of a number. Any positive number $x$ has both a positive and negative square root, which can be written as $\pm \sqrt{x}$.

Examples $\sqrt{64} = 8$ $ \sqrt{9} = 3$ $\sqrt{\frac{4}{25}} = \frac{2}{5}$.

Explanation Every positive number has two dance partners for its square root, one positive and one negative! But the radical symbol $\sqrt{}$ is a bit picky and only wants to dance with the positive partner, which we call the 'principal square root.' So, unless you see a grumpy negative sign outside, always choose the happy, positive root!