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Simplifying Radical Expressions
Simplifying Radicals
Radicals with variables
Definition of Square Root: For any real numbers a and b, if a2 = b, then a is a square root of b.
k aIndex number
Radical sign
radicand
Radical Expression
Let’s review. Simplify each expression. Assume all values of the variable are positive.
Examples:
543).1( 693
693
633
69
Examples:
pp 525 23125).2( p
pp 525 2
pp 55
Try these with your partner:
nn 2100
nn 2100
nn10
3100).3( n
Try these with your partner:
y5
2
y5
2).4(
y
y
5
5
225
52
y
y
y
y
5
52
Adding and Subtracting Radical Expressions
Radical expressions can be combined (added or
subtracted) if they are like radicals – that is, they
have the same root ________ and the same
________.
Example 5: and are alike. The root
index is _____ for both expressions and the
radicand is _____ for both expressions.
6 65
index
radicand
2
6
Example 6: and are not alike. They
both have the same __________ but the root
_______ are not the same.
To determine whether two radicals are like
radicals, you must first __________ each
radicand.
x4 3 4x
indices
radicand
simplify
Simplify each expression:
(7). 6763
(8). 7278
610
76
(9). 215252 29
(10). 5236573
5257363 5935
Try these with your partner:
(11). 119112114
(12). 3735 xx
113
32x
(13). 7112976 2975
(14). 133106104139
10101312
106104133139
Add or subtract as indicated. Simplify first!
(15). 45457
59457
59457
53457
51257 519
(16). 812502
24122252
24122252
224210
214
2212252
Try these with your partner:
(17). 1822
2922
25
2922
2322
(18). 752274
3252394
32
3252394
352334
310312
(19). yy 1092
y4
yy 1092
yy 1092
yy 1032
yy 106
(20). xx 207805
x56
xx 5475165
xx 5475165
xx 527545
xx 514520