A. Properties

1. Product property:
2. Quotient property:

B. How to Simplify using the Product Property

1. Break the number into its largest perfect square factor and the other factor.
2. Both factors go under a like the product property.
3. Take the square root of the perfect square and leave the other factor under a .

C. How to Simplify using the Quotient Property

1. Reduce the fraction if possible, then apply the quotient property.
2. Simplify each radical.
3. If a radical remains in the denominator:
• Rationalize – means to multiply the numerator and denominator by the radical only that remains in the denominator.
4. Simplify.

D. A radical is simplified when:

1. When the expression (number) under the radical sign has no more perfect square factors other than 1.
2. When there is not a fraction under the radical.
3. When there is not a radical in the denominator of a fraction.