# Radicals and Rational Exponents Review ```Algebra 2
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Date________________ Period____
coefficients.
4
4
1) -2 3 - 3 3
2) 3 6 + 2 6
3) -2 6 - 3 12 + 3 24
4) 3 405 -
4
4
4
5 + 2 64
Write each expression in exponential form. (Exponent over index)
5)
4
2
6)
( 3 4x ) 4
Write each expression in radical form. (Write decimals as a fraction, fractions fall down to the
right)
7) 2
1.2
8) b
5
2
Multiplying radicals: two radicals of the same index being multiplied can be combined under
9) 3 15 &times;
11)
13)
3
15
3
18 &times; 4 3
10)
15 &times; -4 5
4
4
12) - 15 &times; - 54
5 (3 - 3 6 )
Dividing radicals: first see if you can simplify the radicals, then cancel common factors in the
top and bottom.
4
2
14)
15)
5 9
2 81
4
2 256
3
16)
2 -4
3
17)
2 108
2 20
125
Worksheet by Kuta Software LLC
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Rationalize a monomial denominator: if the radical in the denominator won't simplify out, you
need to multiply the top and bottom by a radical of the same index that will make the exponent
20
18)
3
19)
12
2
4
20)
22)
4 5k 2
4
21)
27k 4
-1 +
5 9r 3
5 15r 2
3x
14x
Rationalize a binomial denominator:you need to multiply the top and bottom by the conjugate
of the denominator (same terms but opposite sign in the middle), which will leave in the
denominator the first term squared minus the last term squared.
2
23)
5+3 3
-5 +
4
25) -
4
24)
5x -
2x
4
26)
4
3
4
x + 5 3x
Equations with rational exponents: you first need to isolate the base of the exponent on one side
of the equation, then raise both sides to the power of the denominator of the exponent. Then
solve, and make sure if you have to perform a square root or other even-indexed root to include
the + - in your solution.
1
1
3
1
2
27) = b
9
29) 16 = ( p - 22)
28) -7 - 5x = -32
4
3
3
2
30) (v + 20) = 343
Solving radical equations. Just like in equations with rational exponents, first you isolate the
radical on one side of the equation, then square both sides, then solve.
31)
4b - 3 = 3
33)
11 - r =
32) -8 n + 3 = -72
3r - 13
34)
2r - 5 =
r+2
Worksheet by Kuta Software LLC
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1) -5 3
1
4
5) 2
9) 45
13) 3 5 - 3 30
4
17)
5
15r
5
-20 - 4x 2
25)
25x - 2x 3
29) {30, 14}
33) {6}
21)
4
2) 5 6
4
3
6) (4x)
10) -20 3
2
14)
15
15
18)
3
- 14x + x 42
22)
14x
-16 x + 20 3x
26)
59x
30) {29}
34) {7}
3) 4 6 - 6 3
7)
( 5 2 )6
3
4
4
4) 8 5 + 4 4
8)
(
b)
5
4
11) 12 2
3
15)
4
12) 3 10
1
16) 3
6
19)
2
23) -5 + 3 3
27) {81}
4 15k 2
20)
3k
-10 - 2 3
24)
11
28) {125}
31) {3}
32) {78}
4
Worksheet by Kuta Software LLC
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