§7.3 - Adding and Subtracting Radical Expressions
Notes
Radical expressions with sums and differences simplify by combining like
radicals. Like radicals have the same index and the same radicand. For
instance,
√
√
3
3
5 and x 5 are like radicals
But
√
5 and
√
6 are not like radicals.
√
5 and
√
3
5 are not like radicals.
Also,
Two or more like radicals are combined by combining their coefficients.
(Math 1010)
M 1010 §7.3, 7.4
1/7
§7.3 - Adding and Subtracting Radical Expressions
Notes
Examples Combine the radicals, if possible.
√
√
#1 Exercise 7: 9 3 5 − 6 3 5.
√
√
√
√
#2 Exercise 16: 9 3 17 + 7 3 2 − 4 3 17 + 3 2
√
√
#3 Exercise 23: 2 3 54 + 12 3 16
√
√
#4 Exercise 26: 4 y + 2 16y
(Math 1010)
M 1010 §7.3, 7.4
2/7
§7.3 - Adding and Subtracting Radical Expressions
Notes
Examples Perform the addition or subtraction, and simplify your answer.
r
1 √
− 45
#5 Exercise 50:
5
#6 Exercise 53:
√
2
+ 3x
3x
Examples Place the correct symbol. (<, >, or =)
#7 Exercise 58:
(Math 1010)
√
10 −
√
6
√
10 − 6
M 1010 §7.3, 7.4
3/7
§7.4 - Multiplying and Dividing Radical Expressions
Notes
Multiplying radical expressions uses the product rules for radicals, rules for
rational exponents, FOIL, and conjugation.
(Math 1010)
M 1010 §7.3, 7.4
4/7
§7.4 - Multiplying and Dividing Radical Expressions
Notes
Examples Multiply and simplify.
√
√
#1 Exercise 9: 7(3 − 7)
√ √
7( 14 + 3)
√
#3 Exercise 25: ( 20 + 2)2
#2 Exercise 12:
#4 Exercise 30: (3 −
√
5)(3 +
√
5)
√
3
#5 Exercise 41: ( 2x + 5)2
p
√
#6 Exercise 44: ( 3 2y + 10)( 3 4y 2 − 10)
(Math 1010)
M 1010 §7.3, 7.4
5/7
§7.4 - Multiplying and Dividing Radical Expressions
Notes
Conjugates are expressions that differ only by adding and subtracting:
Example 2 +
√
7 and 2 −
√
7 are conjugate expressions.
Recall the rule for multiplying sum and differences:
(a + b)(a − b) = a2 − b 2
Conjugates, when multiplied together, follow this rule.
(Math 1010)
M 1010 §7.3, 7.4
6/7
§7.4 - Multiplying and Dividing Radical Expressions
Notes
Examples Find the conjugate of the expression. Then multiply the
expression by its conjugate and simplify.
#7 Exercise 57: 2 +
#8 Exercise 65:
√
√
5
2u −
√
3
Examples Simplify the expression.
#9 Exercise 75: √
6
11 − 2
#10 Exercise 81: √
(Math 1010)
2
√
6+ 2
M 1010 §7.3, 7.4
7/7
Notes
Notes