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Mathematics for Technology II (Math 2131)

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Study Force Academy
Durham College, Mathematics
Free
  • 36 lessons
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  • 14 week duration

Rules of Radicals

There are several rules of radicals, which are similar to the laws of exponents and, in fact, are derived from them. The first rule is for products.

Root of a Product

Take, for example, (x·y)ⁿ. In the past, you learned that any monomial (i.e. x·y) raised to a single power can be represented as a product of its factors individually raised to that power. Therefore, (x·y)ⁿ is the same as xⁿ·yⁿ. If ⁿ were a fraction, the same rules would apply; remember that fractional exponents can be represented as radicals:

Example 1:

xy12=x12y12=xy=x·y

Example 2:

9x12=912x12=9x=3x

Generally:

ab1n=a1nb1n=anbn

Rooting of a Quotient

To root a fraction, follow the pattern shown below:

abn=anbn=a1nb1n=ab1n

Example:

w25=w25=±w5

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