MA099 - Spring2012
7.5 Expressions Containing Several Radical Terms
Keynote

Adding and Subtracting Radical Expressions

Products and Quotients of Two or More Radical Terms

Rationalizing Denominators and Numerators (Part 2)

Terms with Differing Indices
Adding and Subtracting Radical Expressions
When two radical expressions have the same indices and radicands, they are said to be like radicals.
Like radicals can be combined (added or subtracted) in the same way that we combined like
terms earlier in this text.
Example Simplify by combining like radical terms.
a) 3 5  7 5
3
3
3
b) 7 9s 2  9s 2  2 9 s 2
Example Simplify by combining like radical terms.
a) 2 18  7 2
3
b) 10 3 3m  24m4
Products and Quotients of Two or More Radical Terms
The procedure for multiplying out such expressions is similar to finding products of polynomials.
Example Multiply
2( y  7)
a)
b)
c)
 3 x  2  3 x2  3 

m n

m n

Definition Pairs of radical terms like,
m  n and m  n , are called conjugates.
Rationalizing Denominators and Numerators (Part 2)
The use of conjugates allows us to rationalize denominators or numerators with two terms.
Example
Rationalize the denominator:
5
.
7y
Simplify Products or Quotients with Differing Indices
1. Convert all radical expressions to exponential notation.
2. When the bases are identical, subtract exponents to divide and add exponents to multiply.
This may require finding a common denominator.
3. Convert back to radical notation and, if possible, simplify.
Example Multiply and, if possible, simplify:
5
x x3 .
Solution:
5
x x3  x1/ 2  x3/ 5  x11/10

10 11

10 10 10
x  x
x
 x10 x