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Adding and Subtracting Radicals definitions

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  • Radical
    A mathematical expression involving a root, such as a square root or cube root, indicated by a radical symbol.
  • Radicand
    The value or expression inside the radical symbol that is being rooted, such as the 7 in square root of 7.
  • Index
    The small number written above and to the left of the radical symbol, indicating the degree of the root.
  • Like Radicals
    Radical expressions with identical radicands and indexes, allowing them to be combined through addition or subtraction.
  • Unlike Radicals
    Radical expressions with different radicands or indexes, which cannot be directly combined.
  • Perfect Power
    A number that can be expressed as an integer raised to an exponent matching the radical's index, such as 4 for square roots.
  • Simplification
    The process of rewriting a radical expression by factoring out perfect powers to make combining possible.
  • Square Root
    A radical with an index of 2, representing a value that, when multiplied by itself, gives the radicand.
  • Cube Root
    A radical with an index of 3, representing a value that, when used three times in multiplication, gives the radicand.
  • Constant
    A fixed numerical value in an expression, often appearing as a coefficient in front of a radical.
  • Coefficient
    The numerical factor placed in front of a radical, indicating how many times the radical is counted.
  • Product
    The result of multiplying two or more values, often used when breaking down radicands for simplification.
  • Expression
    A combination of numbers, variables, and mathematical operations, including radicals, that represents a value.
  • Addition
    The operation of combining values, only possible for like radicals by summing their coefficients.
  • Subtraction
    The operation of removing values, only possible for like radicals by subtracting their coefficients.