Square roots (other)

The square root of a positive number $a$ is a number $x$ such that $x^2 = a$. If $a$ is not a perfect square, its square root is irrational. We can estimate or represent these roots using decimals or surds (radicals), like $\sqrt{2}$.

Important properties

• Every positive real number has exactly one positive square root, called the principal square root.

• Square roots of non-square numbers are irrational.

• The square root function is only defined for non-negative real numbers in basic arithmetic.

• $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ for $a, b \geq 0$.

• Square roots can be simplified by factoring out perfect squares.