Supercharge your learning!

Use adaptive quiz-based learning to study this topic faster and more effectively.

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.

$$$ \sqrt[\Tred{3}]{\Tblue{64}} = 4,\quad 4^\Tred{3} = \Tblue{64},\qquad \sqrt[\Tred{3}]{\Tblue{-27}} = -3,\quad (-3)^{\Tred{3}} = \Tblue{-27}.$$$
The side length of a square is the positive square root of its area.
The side length of a square is the positive square root of its area.