# Square and cube roots

The square root of a number is a value that, when squared, equals the original number.

A positive number has **two opposite square roots**.

$$4$$ has two square roots $$2$$ and $$-2$$, because $$$ 2^\Tred{2} = \Tblue{4},\quad (-2)^\Tred{2} = \Tblue{4}.$$$

Zero has one square root. A negative number has no real square root.

$$-2$$ has no square root. $$0$$ is the only square root of $$0$$!

The **positive** square root of $$a$$ is written $$\sqrt{a}$$.

The square roots of $$2$$ are $$\sqrt{2}$$ and $$-\sqrt{2}$$.

The cube root of a number is the value that, when cubed, equals the original number. The cube root of $$a$$ is written $$\sqrt[3]{a}$$.

Positive and negative numbers have **exactly one** cube root.

The side length of a square is the positive square root of its area.