Entire and Mixed Radicals

F. Entire and Mixed Radicals

Sometimes, it is best to retain the exact value of an Irrational radical when performing math operations like adding, subtracting, multiplying, or dividing.

Radicals can be expressed in two forms:

Entire Radical - a radical expression with the entire value sitting under the radical sign.

Mixed Radical - a radical expression, usually written in simplest form, that has a coefficient in front of the radical sign and a value under the radical sign.

The mixed radical is in simplest form.

The entire radical cannot be further simplified to a mixed radical. The reason for this will be made clear in the following examples.

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