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Multiplying, Dividing, and Rationalizing Radicals definitions

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  • Radical
    A mathematical symbol representing the root of a number, often used to indicate square roots or higher roots.
  • Denominator
    The bottom part of a fraction, indicating how many equal parts the whole is divided into.
  • Numerator
    The top part of a fraction, showing how many parts are being considered.
  • Perfect Square
    A value obtained when a number is multiplied by itself, resulting in a whole number under a radical.
  • Rational Number
    A value that can be expressed as a fraction with integers in both the numerator and denominator.
  • Conjugate
    A binomial formed by changing the sign between two terms, used to eliminate radicals in denominators.
  • Binomial
    An algebraic expression containing exactly two terms, often separated by a plus or minus sign.
  • Difference of Squares
    A pattern where two squared terms are subtracted, allowing simplification when multiplying conjugates.
  • FOIL
    A method for multiplying two binomials by combining First, Outer, Inner, and Last terms.
  • Expression
    A combination of numbers, variables, and operations without an equality sign.
  • Fraction
    A numerical quantity expressed as one value divided by another, with a numerator and denominator.
  • Standard Form
    A way of writing mathematical expressions where denominators contain no radicals.
  • Equivalence
    A property where two expressions represent the same value, even if they look different.
  • Square Root
    A value that, when multiplied by itself, gives the original number under the radical.
  • Simplification
    The process of rewriting an expression in a more concise or standard form, often by removing radicals from denominators.