Algebra I Recipe: Simplifying Radicals

1. Product property:
2. Quotient 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 .

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.

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.