Simplifying Different Types of Radical Expressions
Subject:
Algebra [1]
SIMPLIFYING RADICALS Simplest form Similar radicals 2nd level ? Simplifying powers Factors?of the radicand Fractional radicand WE SAY THAT A SQUARE ROOT RADICAL?is?simplified, or in its?simplest form, when the?radicand?has no?square?factors. A radical is also in simplest form when the radicand isnot a fraction. Example 1.???33, for example, has no square factors. ?Its factors are 3??11, neither of which is a square number. ?Therefore,??is in its simplest form. Example 2.???18 has the square factor 9. ?18 = 9??2. ?Therefore,??is not in its simplest form.? To put a radical in its simplest form, we make use of this theorem: The square root of a product? is equal to the product of the square roots? of each factor. (We will prove that when we come to?rational exponents, Lesson 29.