Algebra 2
Name___________________________________ ID: 1
©Q z2p0D1D9a VKVultgaf kSpoufxtswcauryeZ WLyLrCN._ F `AUlJlF CraicgChmtMsn grQeYsZe]rmvZeHdJ.
Assignment: Radicals Review
Date________________ Period____
Adding or subtracting radicals: simplify to get like radicals, then just add or subtract
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
one radical. Then simplify.
9) 3 15 ×
11)
13)
3
15
3
18 × 4 3
10)
15 × -4 5
4
4
12) - 15 × - 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
-1-
©B _2q0p1n9r pKGunt`ab qSLoJf[tYwbairTen jL^L_Cb.n P mA_lclE Pr[i]gmh`tssz ]rGemsFearzvdeod`.m N VM_aAdNe\ PwdiqtKht rIInGfviOnLiqtweH mAilWgpeAbLrUaB y2N.
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
of the radicand the same as the index of the radical.
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
-2-
©W y2J0U1u9H qKIuBtIao [SGo\fjtRw]arrYeH jLxLeCp.n \ jAPlBlx IrmiZg[hftssS RrUebsteqrGveekdu.C g lMNaidiec xwxiTtQhe tITnZf]ifn^ipt[eu GAdlog_esbirqaH i2].
Answers to Assignment: Radicals Review (ID: 1)
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
-3-
©b k2u0o1p9Q ^KZuRtYaO qSooHfXtQweaurCev HLjLuCZ.G P _AUlgl` yrfixggh_tXso wr_eWsneKrWvIeFd_.\ p fM_andmeg owXi^tNht lIXnufriEneiztIeq rAUlQgEelbbrnaW h2e.