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) √3242) √2423) √1474) √405
5) √2526) √1767) √3258) √256
9) √28810) √32011) √58812) √224
13) 4√180 + 3√40514) 7√54 – 6√486
15) 6√150 - 5√21616) 3√432 + 5√128
17) 13√363 + 7√19219) 4√720 - 8√180
19) 7√20 - 3√7520) 5√242 + 7√147
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) √x2414) √x1315) √x3016) √x51
Now combine the two:
17) √363x2018) √80x1919) √289x3620) √72x49
21) √512x2922) √125x3223) √147x4224) √625x13
25) √338x22y1126) √112x19y3127) √361x16y10028) √320x43y21
Simplify Each Radical:
1) √482) √1283) √3634) √45
5) √25x26) √72x87) √432x16y88) √392x100y210
9) √x910) √x9y1011) √x9y1112) √25x9y11
13) √162x10y514) √75x7y315) √300x5y1216) √169x100y64
17) √108x16y2518) √98x1000y50019) √600x11y1420) √288x36y144
21) √300 + √10822) √96 - √150
23) √45 + √2024) √98 - √50
25) 4√200 - 3√28826) 8√392 + 11√32
27) √75x9 - √3x928) 5√363x25 - 4√432x25
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)
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)
Division:
1)Divide numbers 1st to see if you can reduce fraction.
2)Reduce each radical that is left.
3)Cancel where you can.
4)If there is still a radical in the denominator after canceling, you must RATIONALIZE THE DENOMINATOR.
9) 9√294 _10) 14√90 _11) 12√450
7√486 3√245 5√216
12) 13√605 _13) 5√243 _14) 7√96__
33√338 18√384 4√392
15) 16)
17)18)
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. 2. 3.
4. 5. 6.
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 _3) 7√216__
25√200 27√294 4√392
4) 5)
6)7)
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