Radical Workshop Worksheet (Page 2 of 4) in pdf

Radical Workshop Worksheet Page 2

ADDITION AND SUBTRACTION:

Radicals may be added or subtracted when they have the same index and the same radicand (just like

combining like terms).

Note: When adding or subtracting radicals, the index and radicand do not change.

Examples:

MULTIPLICATION OF RADICALS:

To multiply radicals, just multiply using the same rules as multiplying polynomials (Distributive Property, FOIL,

and Exponent Rules) except NEVER multiply values outside the radical times values inside the radical.

Examples:

Note: When multiplying radicals with different indexes, change to rational exponents first, find a common

denominator in order to add the exponents, then rewrite in radical notation as shown below:

Example:

MORE RATIONALIZING THE DENOMINATOR: (DIVISION)

If the denominator contains two terms such that at least one term has a radical, multiply the numerator and

the denominator by the conjugate of the denominator:

Conjugate – the conjugate of a binomial of the form

Example: the conjugate of

Note: Since

, eliminating the middle term, multiplying by the conjugate eliminates

the middle term that would still have a radical in it, thus removing the radical from the denominator.

Examples:

Radical Workshop Worksheet Page 2