1. § 9.4
Rationalizing the Denominator

2. Rationalizing the Denominator
It is sometimes easier to work with radical expressions if the denominators do not contain any radicals.
The process of rewriting a radical expression as an equivalent rational expression with no radicals in the denominator is called rationalizing the denominator.
Blitzer, Introductory Algebra, 5e – Slide #2 Section 9.4

3. Rationalize the Denominator:
Rationalizing the Denominator
Rationalize the Denominator:
EXAMPLE
Any number divided by itself is 1. Multiplication by 1 does not change the value of the expression.
The denominator contains no radicals, we have rationalized the denominator.
Blitzer, Introductory Algebra, 5e – Slide #3 Section 9.4

4. Rationalize the Denominator:
EXAMPLE
Notice what we multiplied by to get rid of the square root
of 2 in the denominator.
When we multiply a square root by itself we get an answer
containing no radicals. For monomial denominators
containing square roots, your choice for multiplication can
just be that square root over itself. But you should simplify
first as we did here – or your problem may be
messier than it needs to be.
The denominator contains no radicals, we have rationalized the denominator.
Blitzer, Introductory Algebra, 5e – Slide #4 Section 9.4