Multiplying and dividing radicals worksheet with answers

Multiplying and dividing radicals makes use of the "Product Rule" and the "Quotient Rule" as seen at the right. The "n" simply means that the index could be any value. Our examples will be using the index to be 2 (square root).

Product Rule

"The radical of a product is equal to the product of the radicals of each factor."

Quotient Rule

"The radical of a quotient is equal to the quotient of the radicals of the numerator and denominator."

ANSWER:

Multiply under the radicals.

Distribute across the parentheses. Remember there is an implied "1" in front of

Use the distributive property to multiply. Combine like terms.

Use the distributive property to multiply. There are NO like terms to be combined.

Dividing Radicals: When dividing radicals (with the same index), divide under the radical, and then divide in front of the radical (divide any values multiplied times the radicals).

ANSWER:

Divide out front and divide under the radicals.

ANSWER:

This fraction will be in simplified form when the radical is removed from the denominator. You need to create a perfect square under the square root radical in the denominator by multiplying the top and bottom of the fraction by the same value (this is actually multiplying by "1"). The easiest approach is to multiply by the square root radical you need to convert (in this case multiply by

Rationalize the denominator is the concept used to simplify a fraction with a square root or cube root in the denominator. It is the process of removing the root from the denominator. You are creating a "rational" number in the denominator instead of an "irrational" number.