Download Name Date AE-255 Additional Exercises 7.1 Form I Radical

Name __________________________________
Date _________________________
Additional Exercises 7.1
Form I
Radical Expressions and Functions
Find the indicated root or state that the expression is not a real number.
1.
49
1. _______________
2.
− 64
2. _______________
3.
3
− 27
3. _______________
4.
3
64
4. _______________
5.
4
16
5. _______________
6.
4
− 16
6. _______________
7.
6
64
7. _______________
8.
5
− 243
8. _______________
Simplify each expression. Include absolute value bars where necessary.
9.
(−3) 2
9. _______________
10.
( x + 4) 2
10. _______________
AE-255
Name __________________________________
Date _________________________
11.
3
( a + 7) 3
11. _______________
12.
5
m5
12. _______________
4x 2
13. _______________
13.
14.
4
( x + 6) 4
14. _______________
15.
3
− 27x 3
15. _______________
16.
− 3 − 64
16. _______________
Find the indicated function values for each function. If necessary round to two decimal places. If
the function value is not a real number and does not exist, so state.
17.
f ( x) = x − 8 ; f (44)
17. _______________
18.
g ( x) = x − 25 ; g (25)
18. _______________
19.
h( x) = 3 5 x − 12 ; h (4)
19. _______________
20.
p ( x) = 3 2 x − 19 ; p (–4)
20. _______________
AE-256
Name __________________________________
Date _________________________
Additional Exercises 7.2
Form I
Rational Exponents
Use radical notation to rewrite each expression. Simplify if possible.
1
1.
64 2
1. _______________
2.
27 3
3.
(5 xy ) 2
4.
32 5
1
2. _______________
1
3. _______________
2
4. _______________
Rewrite the expression with a rational exponent.
5.
10
5. _______________
6.
5
4x
6. _______________
7.
3
82
7. _______________
8.
( 16 )
5
4
8. _______________
Rewrite the expression with a positive rational exponent. Simplify, if possible.
9.
10.
49
16
−
−
1
2
9. _______________
3
4
10. _______________
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Name __________________________________
11.
12.
(−27)
100
−
−
2
3
Date _________________________
11. _______________
3
2
12. _______________
Use the properties of rational exponents to simplify each expression. Assume that all variables
represent positive numbers.
13.
14.
1
8
x x
a
a
7
8
13. _______________
4
5
14. _______________
1
5
1
15.
(100 x 8 y 4 ) 2
16.
& −43 −32 #
$x y !
$
!
%
"
15. _______________
−12
16. _______________
Use rational exponents to simplify each expression. If rational exponents appear after
simplifying, write the answer in radical notation.
17.
10
x5
17. _______________
18.
20
(3 y ) 4
18. _______________
19.
3
x ⋅9 x
19. _______________
20.
10
3
20. _______________
10
AE-262
Name __________________________________
Date _________________________
Additional Exercises 7.3
Form I
Multiplying and Simplifying Radical Expressions
Use the product rule to multiply.
1.
2.
3
3.
4.
3
6⋅ 5
1. _______________
4 ⋅3 3
2. _______________
( x + 4) ⋅ ( x − 4)
3. _______________
3x ⋅ 3 2 x
4. _______________
Simplify. Assume that any variable in the radicand represents a positive real number.
5.
90
5. _______________
6.
108
6. _______________
7.
45 x
7. _______________
8.
3
2 xy 2 ⋅ 3 2 xy 2 ⋅ 3 20 xy 2
8. _______________
9.
3
24 x12
9. _______________
10.
3
48 x 6 y 7
10. _______________
AE-267
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Date _________________________
11.
4
x 4 y 8 z 10
11. _______________
12.
5
( a + b) 7
12. _______________
Express the function in simplified form. Assume that x can be any real number.
13.
f ( x) = ( x − 1) 4
13. _______________
14.
f ( x) = 100( x + 3) 8
14. _______________
15.
f ( x) = x 2 + 4 x + 4
15. _______________
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
16.
5 ⋅ 12
16. _______________
17.
18 ⋅ 6
17. _______________
18.
7 x ⋅ 12 y 2
18. _______________
19.
3
12 x 2 ⋅ 3 4 xy 5
19. _______________
20.
4
5 x 5 y 5 ⋅ 4 32 xy 3
20. _______________
AE-268
Name __________________________________
Date _________________________
Additional Exercises 7.4
Form I
Adding, Subtracting and Dividing Radical Expressions
Add or subtract as indicated. Assume all variables represent positive real numbers.
1.
5 5 +3 5
1. _______________
2.
6 7 − 7 +2 7
2. _______________
3.
4 3 6 − 23 6
3. _______________
4.
2 5 + 43 5 − 6 5
4. _______________
5.
3 5 + 4 125
5. _______________
6.
3
8 y − 3 27 y
6. _______________
7.
5 8 x 3 y + 2 x 32 xy
7. _______________
8.
4 12 − 2 48
8. _______________
Use the quotient rule to simplify. Assume all variables represent positive real numbers.
9.
25
4
9. _______________
10.
13
25
10. _______________
AE-273
Name __________________________________
Date _________________________
3
8
11. _______________
12.
14
x2
12. _______________
13.
50
49
13. _______________
14.
12
81
14. _______________
16
y6
15. _______________
11.
15.
3
3
Divide and simplify. Assume that all variables represent positive real numbers.
16.
17.
18.
19.
20.
100
16. _______________
4
121
17. _______________
11
80
18. _______________
5
32 x 7
19. _______________
4x
150 x 11
20. _______________
3x 5
AE-274
Name __________________________________
Date _________________________
Additional Exercises 7.5
Form I
Multiplying with More Than One Term and Rationalizing Denominators
Multiply as indicated and then simplify if possible. Assume that all variables represent positive
real numbers.
1.
3( 7 + 5 )
1. _______________
2.
5( 6 − 5)
2. _______________
4 (3 3 + 3 2
3. _______________
3.
3
4.
3 3( 7 − 2 2 )
4. _______________
( 11 + 5)( 11 − 5)
5.
5. ______________
6.
( 5 + 2) 2
6. _______________
7.
( 15 + 6 )( 15 − 6 )
7. _______________
Rationalize each denominator. Simplify if possible. Assume that all variables represent positive
real numbers.
1
8.
9.
10.
8. _______________
5
3
6
x
9. _______________
2
3
10. _______________
AE-279
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Date _________________________
11.
3
5x
16 x 2
11. _______________
12.
3
1
4x
12. _______________
13.
14.
15.
16.
3
13. _______________
5− 7
5
14. _______________
8− 3
4
15. _______________
3− 2
2 5
16. ______________
5+2
Rationalize each numerator. Assume that all variables represent positive real numbers.
17.
18.
19.
20.
7
17. _______________
5
5
2
18. _______________
3 2
19. _______________
3
11
7a
20. _______________
AE-280
Name __________________________________
Date _________________________
Additional Exercises 7.6
Form I
Radical Equations
Solve each radical equation.
1.
x =5
1. _______________
2.
x+3 =6
2. _______________
3.
y +1 = 9
3. _______________
4.
x −1 −1 = 7
4. _______________
5.
y−4 =5
5. _______________
6.
5x − 4 = 4
6. _______________
7.
2 x + 1 = 19
7. _______________
8.
6 x + 1 − 11 = 0
8. _______________
9.
8 x + 3 = −6
9. _______________
10.
x +4=9
10. _______________
AE-285
Name __________________________________
3x + 1 − 3 = 1
11.
12.
Date _________________________
11. _______________
1
2
(4 x + 8) = 4
12. _______________
1
2
13.
(a − 3) + 6 = 7
14.
3
3x + 4 = 7
14. _______________
15.
3
5x + 2 = 3
15. _______________
16.
4
4x + 1 = 3
16. _______________
17.
a−3 = a−3
17. _______________
18.
(5 x + 1) 2 = x + 1
18. _______________
19.
x + 7 = 2 x + 13
19. _______________
13. _______________
1
20.
x+5 = x−3 +2
20. _______________
AE-286
Name __________________________________
Date _________________________
Additional Exercises 7.7
Form I
Complex Numbers
Express each number in terms of i and simplify if possible.
1.
− 25
1. _______________
2.
− 121
2. _______________
3.
− 32
3. _______________
4.
− 50
4. _______________
5.
7 + − 18
5. _______________
Perform the indicated operations. Write the results in the form a + bi .
6.
(8 + 2i ) + (2 + 8i )
6. _______________
7.
6i − (8 − 3i )
7. _______________
8.
(10 − 3i ) − (4 − 6i )
8. _______________
9.
5(2 − 3i )
9. _______________
10.
3i (4 − 8i )
10. _______________
AE-291
Name __________________________________
Date _________________________
11.
(2 − 9i )(8 + 4i )
11. _______________
12.
(4 − 5i ) 2
12. _______________
Divide and simplify to the form a + bi .
13.
5 + 8i
4 − 2i
13. _______________
14.
3 + 2i
2 − 5i
14. _______________
15.
3 − 4i
i
15. _______________
16.
6 − 5i
3i
16. _______________
Simplify each expression.
17.
i6
17. _______________
18.
i 20
18. _______________
19.
i 27
19. _______________
20.
(−i ) 5
20. _______________
AE-292