How to Simplify Radicals for Higher Algebra, Step by Step

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In math, when the same number is multiplied together many times, this is known as a power operation. For example, if you multiply 2 by itself twice, then this can be written as 2 to the power of 2 (2^2), and the result is equal to 4. The inverse operation can be applied by obtaining the "root" or the radical. For example, the radical (or square root) of 4 reverses the power operation, yielding 2. Radicals can be simplified using a set of straightforward mathematical rules.

Things You'll Need

  • Pen
  • Paper
  • Write out the rules for radicals. The product rule states that two radicals can be multiplied together if they have the same root:

    n√a x n√b = n√ab

    The quotient rule states that two radicals can be divided if they have the same root:

    n√a / n√b = n√(a/b)

    These rules apply to numbers as well as algebraic expressions.

  • Write down the radical that needs to be simplified. For the sake of this example, let's assume that the radical is an algebraic expression: 2√(4a^3).

  • Use the product and quotient rules to split the radical into simpler components. Following the example, 2√(4a^3) can be written as a product:

    2√(4a^3) = 2√(4 x a x a^2) = 2√4 x 2√(a^2) x 2√a

  • Evaluate as many terms as possible within the product. Following the example, we know that the radical of 4 is equal to 2 and that the radical of a-squared is equal to a:

    2√4 x 2√(a^2) x 2√a = 4 x 2a x (2√a)

References

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