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
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)
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