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 Depdendent Variable

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 Dependent Variable

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# Simplifying Radical Expressions Containing One Term

Here is what we mean by the simplified form of a radical expression that contains one term.

Definition â€” Simplified Form of a Radical Expression That Contains One Term

A radical expression that contains one term is in simplified form when:

â€¢ For there are no factors of x, other than 1, that are perfect nth powers.

â€¢ There are no fractions under the radical symbol.

â€¢ There are no radicals in the denominator of an expression.

 Here are some examples: Not simplified â€¢ For there are no factors of x, other than 1, that are perfect nth powers. â€¢ There are no fractions under the radical symbol. â€¢ There are no radicals in the denominator of a fraction.

Example

Simplify:

Solution
 This radical is a cube root. It is not in simplified form because the radicand has some factors that are perfect cubes. To begin, we identify those factors. Factor the radicand. Use perfect cube factors when possible. Write as a product of radicals. Place each perfect cube under its own radical symbol. You can leave the â€œnoncubeâ€ factors under the same radical symbol. Simplifying the cube root of each perfect cube. Multiply the factors outside the radical symbol. So,