2 rules for radicals
TRANSCRIPT
Algebraic Expressions - Rules for Radicals
Let’s review some concepts from Algebra 1.
b
a
b
a
If you have the same index, you can rewrite division of radical expressions to help simplify. This rule also applies in the opposite direction.
Algebraic Expressions - Rules for Radicals
Let’s review some concepts from Algebra 1.
b
a
b
a
EXAMPLE # 1 : 392
18
2
18
If you have the same index, you can rewrite division of radical expressions to help simplify. This rule also applies in the opposite direction.
Algebraic Expressions - Rules for Radicals
Let’s review some concepts from Algebra 1.
b
a
b
a
If you have the same index, you can rewrite division of radical expressions to help simplify. This rule also applies in the opposite direction.
EXAMPLE # 1 : 392
18
2
18
baba If you have the same index, you can rewrite multiplication of radical expressions to help simplify. This rule also applies in the opposite direction.
Algebraic Expressions - Rules for Radicals
Let’s review some concepts from Algebra 1.
b
a
b
a
If you have the same index, you can rewrite division of radical expressions to help simplify. This rule also applies in the opposite direction.
EXAMPLE # 1 : 392
18
2
18
baba If you have the same index, you can rewrite multiplication of radical expressions to help simplify. This rule also applies in the opposite direction.
4168282 EXAMPLE # 2 :
Algebraic Expressions - Rules for Radicals
nm
aan m This rule is used to change a radical expression into an algebraic expression with a rational ( fraction ) exponent.
You divide the exponent by the index ( your root )
Remember, if no root is shown, the index = 2
Algebraic Expressions - Rules for Radicals
nm
aan m This rule is used to change a radical expression into an algebraic expression with a rational ( fraction ) exponent.
You divide the exponent by the index ( your root )
Remember, if no root is shown, the index = 2
EXAMPLE # 3 :323 2 xx
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
EXAMPLE # 4 :1632 77 baba
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
EXAMPLE # 4 :
48
1632
49
77
ba
baba
Apply this rule first along with the rule for multiplying variables…
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
EXAMPLE # 4 :
48
48
1632
49
49
77
ba
ba
baba
Now lets split up each term so you can see it…it’s the rule in the opposite direction
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
EXAMPLE # 4 :
24
48
48
1632
77
49
49
77
24
28
baba
ba
ba
baba
Find the square root of the integer and apply this rule to your variables…no index is shown so it equals two…
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
EXAMPLE # 4 :
24
48
48
1632
77
49
49
77
24
28
baba
ba
ba
baba
The middle steps are not necessary if you want to mentally go from step one to the answer…
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
EXAMPLE # 5 :32
96
6
24
nm
nm
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
EXAMPLE # 5 :32
96
6
24
nm
nm Apply this rule first along with the rule for dividing variables and simplify under the radical…
6432
96
46
24nm
nm
nm
Algebraic Expressions - Rules for Radicals
nm
aan m
We are going to use these rules to simplify expressions. You might have to use all of them together to simplify one problem.
abbab
a
b
a
EXAMPLE # 5 :32
96
6
24
nm
nm
Now apply the index rule…32
6432
96
22
46
24
26
24
nmnm
nmnm
nm
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
First, rewrite using rational exponents….
412
48
46
41
36 cba
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
As you can see, the index of the first and second term are now different…this is not allowed
3223
41
412
48
46
41
3636 cbacba
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
Rewrite 36 as 6 squared…when you apply the rule for an exponent inside raised to an exponent outside, the index will reduce…
322
32
23
41
23
41
412
48
46
41
6
3636
cba
cbacba
21
41
41
666 22
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
Insert this into our problem…
32322
32
23
21
23
41
23
41
412
48
46
41
66
3636
cbacba
cbacba
21
41
41
666 22
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
32322
32
23
21
23
41
23
41
412
48
46
41
66
3636
cbacba
cbacba
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
Writing the answer in radical form :
1. Any integer exponents appear outside the radical
2. Any proper fraction goes under the radical
3. Improper fractions are broken up into an integer and a remainder. The integer part goes outside the radical, the remainder goes inside the radical
32322
32
23
21
23
41
23
41
412
48
46
41
66
3636
cbacba
cbacba
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
Any integer exponents appear outside the radical
66
3636
3232322
32
23
21
23
41
23
41
412
48
46
41
cbcbacba
cbacba
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
666
3636
13232322
32
23
21
23
41
23
41
412
48
46
41
cbcbacba
cbacba
Any proper fraction goes under the radical.To do this, apply the rational exponent rule backwards.Only your exponent will appear…
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
666
3636
3232322
32
23
21
23
41
23
41
412
48
46
41
cbcbacba
cbacba
Improper fractions are broken up into an integer and a remainder. The integer part goes outside the radical, the remainder goes inside the radical.How many 2’s divide 3 with out going over ?
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
666
3636
3232322
32
23
21
23
41
23
41
412
48
46
41
cbcbacba
cbacba
Improper fractions are broken up into an integer and a remainder. The integer part goes outside the radical, the remainder goes inside the radical.How many 2’s divide 3 with out going over ?One with a remainder of one.
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :4 128636 cba
113232322
32
666
3636
23
21
23
41
23
41
412
48
46
41
aacbcbacba
cbacba
Improper fractions are broken up into an integer and a remainder. The integer part goes outside the radical, the remainder goes inside the radical.How many 2’s divide 3 with out going over ?One with a remainder of one.The integer that divides it goes outside, the remainder goes inside…
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :
21
25
61
63
615
66
61 1
6 3156
88
8
zyxzyx
zyx
First, rewrite using rational exponents and reduce any fractional exponents….
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :
21
25
21
21
25
61
21
25
61
63
615
66
61
113
1
6 3156
22
88
8
zyxzyx
zyxzyx
zyx
Now reduce the index of your integer….
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :
22
88
8
1113
1
6 3156
21
25
21
21
25
61
21
25
61
63
615
66
61
xzyxzyx
zyxzyx
zyx
Rewrite your answer in radical form….
Any integer exponents appear outside the radical
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :
111113
1
6 3156
z222
88
8
21
25
21
21
25
61
21
25
61
63
615
66
61
xzyxzyx
zyxzyx
zyx
Rewrite your answer in radical form….
Any proper fraction goes under the radical.To do this, apply the rational exponent rule backwards.Only your exponent will appear…
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :
11121113
1
6 3156
z222
88
8
21
25
21
21
25
61
21
25
61
63
615
66
61
yyxzyxzyx
zyxzyx
zyx
Rewrite your answer in radical form….
Improper fractions are broken up into an integer and a remainder. The integer part goes outside the radical, the remainder goes inside the radical.How many 2’s divide 5 with out going over ?2 with a remainder of 1…
Algebraic Expressions - Rules for Radicals
Reducing the index – sometimes when applying the rule your fractional exponent will change its index due to reducing. When that happens, all indexes must be the same.
EXAMPLE :
zyxyyyxzyxzyx
zyxzyx
zyx
2z222
88
8
211121113
1
6 3156
21
25
21
21
25
61
21
25
61
63
615
66
61
The ones as exponents are not needed in your answer, I put them there so you could see where things were going…