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Study Guides > College Algebra

Key Concepts & Glossary

Key Concepts

  • The principal square root of a number aa is the nonnegative number that when multiplied by itself equals aa.
  • If aa and bb are nonnegative, the square root of the product abab is equal to the product of the square roots of aa and bb
  • If aa and bb are nonnegative, the square root of the quotient ab\frac{a}{b} is equal to the quotient of the square roots of aa and bb
  • 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 aa is the number with the same sign as aa that when raised to the nth power equals aa. 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 aa that when raised to the nth power equals aa principal square root the nonnegative square root of a number aa that, when multiplied by itself, equals aa radical the symbol used to indicate a root radical expression an expression containing a radical symbol radicand the number under the radical symbol  

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