exponents & radicals – rules for radicals a radical is simply a root. the root taken is also...
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Exponents & Radicals – Rules for Radicals
A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three.
Exponents & Radicals – Rules for Radicals
A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three.
For now we will work only with square roots.
Exponents & Radicals – Rules for Radicals
A radical is simply a root. The root taken is also referred to as an index. If you have a square root the index is two. If you have a cube root the index is three.
For now we will work only with square roots.
Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares…
36666
25555
16444
9333
4222
1111
2
2
2
2
2
2
144121212
121111111
100101010
81999
64888
49777
2
2
2
2
2
2
Exponents & Radicals – Rules for Radicals
Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares…
36666
25555
16444
9333
4222
1111
2
2
2
2
2
2
144121212
121111111
100101010
81999
64888
49777
2
2
2
2
2
2
To find a perfect square root, we will think of the perfect square table. Realize that table keeps going, I only went up to 12….
EXAMPLE : 25
Exponents & Radicals – Rules for Radicals
Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares…
36666
25555
16444
9333
4222
1111
2
2
2
2
2
2
144121212
121111111
100101010
81999
64888
49777
2
2
2
2
2
2
To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12….
EXAMPLE : 25 What number did I multiply to get 25 ?
Exponents & Radicals – Rules for Radicals
Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares…
36666
25555
16444
9333
4222
1111
2
2
2
2
2
2
144121212
121111111
100101010
81999
64888
49777
2
2
2
2
2
2
To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12….
EXAMPLE : 525 Notice there is no longer a radical over the answer…
Exponents & Radicals – Rules for Radicals
Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares…
36666
25555
16444
9333
4222
1111
2
2
2
2
2
2
144121212
121111111
100101010
81999
64888
49777
2
2
2
2
2
2
To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12….
EXAMPLE : ?100 What number did I multiply to get 100 ?
Exponents & Radicals – Rules for Radicals
Perfect Squares – numbers that are gotten by multiplying the SAME number by itself. You could create a table of perfect squares…
36666
25555
16444
9333
4222
1111
2
2
2
2
2
2
144121212
121111111
100101010
81999
64888
49777
2
2
2
2
2
2
To find a perfect square root, we will think of the perfect square table. realize that table keeps going, I only went up to 12….
EXAMPLE : 10100 Notice there is no longer a radical over the answer…
Exponents & Radicals – Rules for Radicals
So now we could create a square root table…
12144 636
11121 525
10100 416
981 39
864 24
749 11
Exponents & Radicals – Rules for Radicals
Some rules for radicals :
1. A number / variable, divided by its square root, equals its square root
66
36 5
5
5 a
a
a
Exponents & Radicals – Rules for Radicals
Some rules for radicals :
1. A number / variable, divided by its square root, equals its square root
2. Numbers / variables under THE SAME root / index can be multiplied or divided
66
36 5
5
5 a
a
a
1052
172
34
Exponents & Radicals – Rules for Radicals
Some rules for radicals :
1. A number / variable, divided by its square root, equals its square root
2. Numbers / variables under THE SAME root / index can be multiplied or divided
66
36 5
5
5 a
a
a
1052
172
34
This rule also works in the OTHER direction, and is sometimes used to help simplify radicals…
3412
53
15
3
15
Exponents & Radicals – Rules for Radicals
Some rules for radicals :
3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same.
787627672
Exponents & Radicals – Rules for Radicals
Some rules for radicals :
3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same.
787627672
xxxx 86262 Just like
Exponents & Radicals – Rules for Radicals
Some rules for radicals :
3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same.
787627672
xxxx 86262 Just like
aaa 1385
Exponents & Radicals – Rules for Radicals
Some rules for radicals :
3. Radicals act like variables. They can be added / subtracted as long as the root / index is the same AND what is under the radical is exactly the same.
787627672
xxxx 86262 Just like
aaa 1385
3724
You CAN NOT combine these. The number under the root is NOT the same…
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 1 : Simplify 20
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 1 : Simplify 20
54
102
201
Factors of 20
Method # 1 : 1st – list the factors of 20
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 1 : Simplify 20
54
102
201
Factors of 20
Method # 1 : 1st – list the factors of 20
2nd – find the pair that has the biggest perfect square
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 1 : Simplify 20
54
102
201
Factors of 20
Method # 1 : 1st – list the factors of 20
2nd – find the pair that has the biggest perfect square
3rd - break up your original number into this pair under radicals
5 4
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 1 : Simplify 20
54
102
201
Factors of 20
Method # 1 : 1st – list the factors of 20
2nd – find the pair that has the biggest perfect square
3rd – break up the original number into that pair under radicals
4th – simplify the square root of the perfect square
52
5 4
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 2 : Simplify 80
Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder.
We never use 1…
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 2 : Simplify 80
Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder.
We never use 1…
63.14980
22.23680
2.32580
51680
89.8980
20480
When your answer falls below 2 stop.
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 2 : Simplify 80
Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder.
We never use 1…
63.14980
22.23680
2.32580
51680
89.8980
20480
When your answer falls below 2 stop.
Even though there are two that work, we want the LARGEST perfect square…
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 2 : Simplify 80
Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder.
We never use 1…
63.14980
22.23680
2.32580
51680
89.8980
20480
Break up your number into the perfect square that worked and the result…
5 16
Exponents & Radicals – Rules for Radicals
Simplifying radicals – sometimes a number under a radical can be broken into a perfect square part and a radical part.
EXAMPLE # 2 : Simplify 80
Method # 2 : Go thru the perfect square table and find the LARGEST perfect square that divides your number without a remainder.
We never use 1…
63.14980
22.23680
2.32580
51680
89.8980
20480
Reduce your perfect square…
5 16
54
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