Radical

Definition

A radical is an expression that includes a root, such as a square root or cube root. The most common radical is the square root, denoted by the symbol $\sqrt{}$.

5 Must Know Facts For Your Next Test

1. The expression $\sqrt{a}$ represents the principal square root of $a$, where $a \geq 0$.
2. Radicals can be simplified by factoring out perfect squares, cubes, etc., from under the radical sign.
3. The product and quotient rules for radicals state that $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ and $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$, respectively, given that $a$ and $b$ are non-negative.
4. Rationalizing a denominator involves removing the radical from the denominator of a fraction by multiplying both numerator and denominator by an appropriate value.
5. A radical equation is an equation in which the variable appears inside a radical. Solving such equations often involves squaring both sides to eliminate the radical.

Review Questions

• What does the expression $\sqrt[3]{27}$ simplify to?
• How do you rationalize the denominator of the fraction $\frac{1}{\sqrt{2}}$?
• Describe the process of solving the equation $\sqrt{x + 6} = 4$.

Related terms

Square Root: The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol $\sqrt{}$. For example, $\sqrt{9} = 3$.

Cube Root: The cube root of a number is a value that, when used three times in multiplication, gives that number. It is denoted by the symbol $\sqrt[3]{}$. For example, $\sqrt[3]{8} = 2$.

Rational Exponent: An exponent expressed as a fraction. For example, $x^{1/2}$ represents the square root of x and is equivalent to $\sqrt{x}$.