Simplifying Radicals

A radical expression is in simplest form when: The expression under the radical sign has no perfect square factors other than 1. The expression under the radical sign does not contain a fraction. The denominator does not contain a radical expression.

To simplify a radical: Put like factors in pairs. Find the prime factorization of the number under the radical. For example: Put like factors in pairs. Find the square root of the pairs and place it outside the radical. Multiply numbers on the outside of the radical and multiply numbers on the inside.

Example 1

Example 2

Example 3

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