Key Concepts & Glossary
Key Concepts
- The principal square root of a number is the nonnegative number that when multiplied by itself equals .
- If and are nonnegative, the square root of the product is equal to the product of the square roots of and
- If and are nonnegative, the square root of the quotient is equal to the quotient of the square roots of and
- 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 is the number with the same sign as that when raised to the nth power equals . 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.