section 9.3 multiplying and dividing radical expressions
TRANSCRIPT
Section 9.3 Multiplying and Dividing Radical Expressions
9.3 Lecture Guide: Multiplying and Dividing Radical Expressions
Objective: Multiply radical expressions.
To multiply and divide some radical expressions, we use the properties:
Multiplying Radicals
n n nx y xy for 0x and 0y
n
nn
x x
yy for 0x and 0y
Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0.
1. 32 2
Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0.
2. 2 8x x
Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0.
3. 3 23 27x x
Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0.
4. 3 5 2 3
Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0.
5. 4 5 3 5 7
Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0.
6. 3 3 2 5 5 3
Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0.
7. 8 7 1 2 7 3
Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0.
8. 5 3 5 3y x y x
Simplify each expression. Assume x > 0 and y > 0.
9. 520x
Simplify each expression. Assume x > 0 and y > 0.
10. 3 728x y
Simplify each expression. Assume x > 0 and y > 0.
11. 4 83 16x y
Simplify each expression. Assume x > 0 and y > 0.
12. 5 103 54x y
Objective: Divide and simplify radical expressions.
Dividing Radicals
When dividing radical expressions, we do not always get a result that is rational. In this case, answers are typically given without any radicals in the denominator.
Recall that 2x = ____________ for 0.x In general, n nx _____________ for 0.x
As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication.
13. 2 2
As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication.
14. 8 2
As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication.
15. 3 23 4 4
As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication.
16. 3 2 32 4x x
Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0.
17.2
5
Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0.
18.3
7
Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0.
19.5
2
x
y
Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0.
20. 3
1
2
Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0.
21. 3
4
x
Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0.
22. 3 2
4
2x
Conjugates Radicals: The conjugate of x y is
.x y
Write the conjugate of each expression. Then multiply the expression by its conjugate.
Expression Conjugate Product
23.
24.
25.
Example:
2 32 3
2 3 2 3 4 9
2 3
1
3 5 2 7
3x y
2 3x y
Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers.
26.16
7 3
Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers.
27.8
3 5
Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers.
28.3
2 5
Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers.
29.4x
x y
Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers.
30. 3
5 7x y
Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers.
31.5 2
x
x y
Determine whether or not each value of x is a solution of the equation 2 2 4 0.x x
32. 2x
Determine whether or not each value of x is a solution of the equation 2 2 4 0.x x
33. 2x
Determine whether or not each value of x is a solution of the equation 2 2 4 0.x x
34. 1 5x
Determine whether or not each value of x is a solution of the equation 2 2 4 0.x x
35. 1 3x