Name
Freshman Radicals Packet
Mr. McCormack’s Magical Method of Reducing Radicals
Step 1: Check to see if the number is a perfect square.
 If “yes,” you are done.
 If “no,” go to next step.
Step 2: Divide the number by 2, and check to see if that number is a perfect square.
 If “yes,” you are finished. Just take the square root of the new # and leave “2” under
the radical.
 If “no,” go to next step.
Step 3: Divide the original # by the biggest perfect square less than the # you got when you
divided the # by 2.
 If it goes in evenly, you are finished.
 If it doesn’t go in evenly, go to next step.
Step 4: Keep trying the next biggest perfect square until you get a number that goes in evenly.
Simplify each radical:
1) √324
2) √242
3) √147
4) √405
5) √252
6) √176
7) √325
8) √256
9) √288
10) √320
11) √588
12) √224
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Name
Freshman Radicals Packet
13) 4√180 + 3√405
14) 7√54 – 6√486
15) 6√150 - 5√216
16) 3√432 + 5√128
17) 13√363 + 7√192
19) 4√720 - 8√180
19) 7√20 - 3√75
20) 5√242 + 7√147
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Name
Freshman Radicals Packet
When working with a variable, you have to
check whether the exponent is odd or even.
When Even: You get the square root by cutting the exponent in half.
For example: √x16  x8
When Odd: You factor it by taking one off and making it even (then you can cut it in
half and leave the x under the radical):
For example: √x17  √x16 ∙ x1  x8√x1 OR x8√x
13) √x24
14) √x13
15) √x30
16) √x51
Now combine the two:
17) √363x20
18) √80x19
19) √289x36
20) √72x49
21) √512x29
22) √125x32
23) √147x42
24) √625x13
25) √338x22y11
26) √112x19y31
27) √361x16y100
28) √320x43y21
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Name
Freshman Radicals Packet
Simplify Each Radical:
1) √48
2) √128
3) √363
4) √45
5) √25x2
6) √72x8
7) √432x16y8
8) √392x100y210
9) √x9
10) √x9y10
11) √x9y11
12) √25x9y11
13) √162x10y5
14) √75x7y3
15) √300x5y12
16) √169x100y64
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Name
17) √108x16y25
Freshman Radicals Packet
18) √98x1000y500 19) √600x11y14
20) √288x36y144
21) √300 + √108
22) √96 - √150
23) √45 + √20
24) √98 - √50
25) 4√200 - 3√288
26) 8√392 + 11√32
27) √75x9 - √3x9
28) 5√363x25 - 4√432x25
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Name
Freshman Radicals Packet
Multiplication:
1) (-3√6)(8√12)
2) (5√18)(6√24)
3) 9√2 (6√96 - 4√160)
4) -7√3 (3√150 - 4√18)
5) (9 – 5√5)(8 – 3√5)
6) (4 - 3√2)(7 + 5√6)
7) (8 - 3√2)(9 + 3√2)
8) (-4 + 6√5)(-4 - 6√5)
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Name
Freshman Radicals Packet
Classwork:
1) (-8√8)(5√24)
2) (-6√12)(-4√27)
3) 5√3 (8√150 - 4√294)
4) -9√5 (3√135 - 7√40)
5) (6 – 5√2)(-9 – 3√2)
6) (-3 - 9√3)(10 + 5√6)
7) (11 - 3√6)(4 + 3√6)
8) (-5 + 6√2)(-12 - 6√8)
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Name
Freshman Radicals Packet
Division:
1)
2)
3)
4)
9)
Divide numbers 1st to see if you can reduce fraction.
Reduce each radical that is left.
Cancel where you can.
If there is still a radical in the denominator after canceling, you must RATIONALIZE THE
DENOMINATOR.
9√294 _
10)
7√486
12)
13√605 _
33√338
14√90 _
3√245
13)
5√243 _
18√384
11) 12√450
5√216
14) 7√96__
4√392
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Name
15)
17)
Freshman Radicals Packet
6
7 2
6 3
5 3
16)
18)
6 2
4 5
6 3
3 6
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Name
Freshman Radicals Packet
Quiz Review:
Part I: Reducing Radicals:
1) √882x10y5
2) √245x7y3
3) √252x6y12
4) √289x100y64
5) √432x17y9
6) √605x18y11
7) √529x49y64
8) √800x33y43
9) √294x14y72
10) √980x21y26
11) √507x13y23
12) √361x41y100
Part II: Addition/Subtraction
1. 6 192  9 507
2. 11 405  8 245
3. 4 288  3 512
4. 5 343  4 867
5.  7 384  5 432
6. 3 108  7 675  6 588
Part III: Multiplication
1) (-5√12)(8√5)
2) 9√5 (6√250 - 4√180)
3) -8√2 (3√150 - 4√192)
4) (-7 + 6√3)(-7 - 6√3)
5) (8 – 5√3)(6 – 3√2)
6) (4 - 3√2)(8 + 5√10)
Part IV: Division
1)
10√675 _
2) 21√486 _
25√200
3)
27√294
4)
6)
6
13  3
6 6
12  6
7√216__
4√392
5)
7)
10  3
12  5
12  2
3 6
10