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Simplifying Radical Expressions Containing One
Term

Example

Simplify:

Solution

This radical is not in simplified form because it has a fraction under the
radical symbol.

We cannot simplify the fraction because the numerator and
denominator have no common factors except 1 and -1.
Instead we will write the radical as a quotient of two radicals. Then we
will try to simplify each radical so that we can write the expression
without a radical in the denominator.

Use the Division Property of Radicals
to write the radical as a quotient of
two radicals.

For each radical, factor the radicand.
Use perfect fourth power factors
when possible.

Write as a product of radicals.
Place each perfect fourth power
under its own radical symbol.

Simplify the fourth root of each
perfect fourth power.

Multiply the factors outside
the radical.

So,

There is often more than one way to simplify a radical expression. With
practice, you may be able to decrease the amount of writing required.