Key Concepts

• The principal square root of a number $a$ is the nonnegative number that when multiplied by itself equals $a$.
• If $a$ and $b$ are nonnegative, the square root of the product $ab$ is equal to the product of the square roots of $a$ and $b$
• If $a$ and $b$ are nonnegative, the square root of the quotient $\frac{a}{b}$ is equal to the quotient of the square roots of $a$ and $b$
• We can add and subtract radical expressions if they have the same radicand and the same index.
• Radical expressions written in simplest form do not contain a radical in the denominator. To eliminate the square root radical from the denominator, multiply both the numerator and the denominator by the conjugate of the denominator.
• The principal nth root of $a$ is the number with the same sign as $a$ that when raised to the nth power equals $a$. These roots have the same properties as square roots.
• Radicals can be rewritten as rational exponents and rational exponents can be rewritten as radicals.
• The properties of exponents apply to rational exponents.

Glossary

index the number above the radical sign indicating the nth root

principal nth root the number with the same sign as $a$ that when raised to the nth power equals $a$

principal square root the nonnegative square root of a number $a$ that, when multiplied by itself, equals $a$

radical the symbol used to indicate a root

radical expression an expression containing a radical symbol

radicand the number under the radical symbol