Lesson 4

Lesson 4 Summary

 

The same rules used for multiplying and dividing monomials, binomials, and polynomials in previous math courses also apply to radicals.

 

When multiplying and dividing radicals, you need to work with both the coefficients and the radicands. The key to multiplying and dividing radicals is to be sure that they have the same index. Just as you can’t mix apples and oranges, you can’t multiply or divide radicals that have different indices.

 

When multiplying radicals, first multiply the coefficients, and then multiply the radicands. When dividing radicals, first divide the coefficients, and then divide the radicands. In both cases, you must always simplify your answer so that the radical is in lowest terms.

 

You also looked at restrictions on the variables in radicals. If the index is an even number, the radicands cannot have a negative number. If the index is an odd number, the radicand could be negative or positive, so there are no restrictions on the variable. The exception to this is when you have a variable in the denominator because division by zero is undefined. If there is a variable in the denominator, then you must state the restriction that the variable cannot equal zero.

 

In the next lesson you will simplify fractional radicals further by learning to write them without a radical in the denominator.