Radical

Definition

A radical is an expression that uses a root, such as the square root or cube root, to indicate a value that, when raised to a specified power, yields the original number. Radicals are often used to simplify expressions and solve equations involving roots.

5 Must Know Facts For Your Next Test

1. The square root of a number $x$ is written as $\sqrt{x}$ and represents the value that, when squared, equals $x$.
2. Cube roots are denoted as $\sqrt[3]{x}$ and represent values that, when cubed, equal $x$.
3. The expression $\sqrt[n]{x}$ represents the $n^{th}$ root of $x$, which is a value that, when raised to the power of $n$, equals $x$.
4. Rational exponents can be used in place of radicals; for example, $x^{1/n}$ is equivalent to $\sqrt[n]{x}$.
5. Simplifying radicals involves finding the largest perfect square (or other relevant power) factor of the radicand and rewriting the radical as a product.

Review Questions

• What does $\sqrt{49}$ simplify to?
• Rewrite $\sqrt[4]{16}$ using a rational exponent.
• Simplify the expression: $\sqrt{50} + \sqrt{18}$.

Related terms

Square Root: A value that, when multiplied by itself, gives the original number. Represented by $\sqrt{x}$.

Radicand: The number or expression inside a radical symbol. For example, in $\sqrt{25}$, 25 is the radicand.

Rational Exponent: $An exponent expressed as a fraction where $a^{m/n} = \left(\sqrt[n]{a}\right)^m$. Used interchangeably with radicals.$