Simplifying Fractional Radicals and Radicals with Variables
Recall the definition of simplified radical form and write it here.
Radicals with Variables
Consider a radical with variables
Factor out the perfect square(s).
18x3
Rewrite the expression as the product of 2 square roots one with the perfect square factors and one with
the other factors
Rewrite the expression with the perfect square factors simplified
Example: Simplify
3
54 x4 y 2 z 5
Fractional Radicals
Consider the following radical
2
Is this in simplified form? Why or why not?
5
Use the rules of exponents to rewrite this as 2 separate radicals one in the numerator and one in the
denominator.
Use what you have learned about rationalizing denominators to rewrite it in simplified radical form.
Example
3
8
7
Fractional Radicals with Variables
Consider the expression
3
3
2x2
Use the laws of exponents to rewrite this expression as two radicals, one in the numerator and one in the
denominator.
Use what you have learned to rationalize the denominator
Use the properties of exponents and algebraic simplification to simplify the resulting expression
Example:
3
96
3xy 2