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Simplifying Radical Expressions definitions

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  • Radical
    Mathematical symbol representing the root of a number or expression, such as a square root or cube root.
  • Radicand
    The value or expression located inside a radical symbol, whose root is being taken.
  • Index
    The small number written above and to the left of the radical sign, indicating the degree of the root.
  • Perfect Square
    A number or expression that is the square of an integer or variable, allowing for exact square root extraction.
  • Perfect Cube
    A value that results from raising an integer or variable to the third power, enabling exact cube root extraction.
  • Exponent
    A number indicating how many times a base is multiplied by itself, often used to simplify radicals with variables.
  • Product Rule for Radicals
    Property allowing the radical of a product to be written as the product of separate radicals.
  • Quotient Rule for Radicals
    Property allowing the radical of a fraction to be written as the quotient of separate radicals.
  • Like Radicals
    Radical expressions with identical radicands and indexes, making them eligible for addition or subtraction.
  • Unlike Radicals
    Radical expressions with different radicands or indexes, requiring simplification before combining.
  • Simplified Radical Form
    A radical expression in which all possible perfect powers have been extracted and no further simplification is possible.
  • Variable
    A symbol, often a letter, representing an unknown value, which can appear under a radical and be simplified using exponent rules.
  • Fractional Radicand
    A radicand that is a fraction, which can be split into separate radicals for numerator and denominator.
  • Addition of Radicals
    Operation combining like radicals by adding their coefficients, similar to combining like terms in algebra.
  • Subtraction of Radicals
    Operation combining like radicals by subtracting their coefficients, only possible when radicands and indexes match.