Download Unit 6 Day B

WHRHS
2011-2012
Unit 6 - Radicals
Algebra 2A
Unit 6 ~ Day B ~ Simplifying Radicals
A. Simplifying Radicals –
1. Perfect Radicands – The product of a number multiplied by itself however many times the given index
4  2 (4 is a perfect square & 2 is the square root),
3
8  2 (8 is a perfect cube & 2 is the cube root),
5
32  2 (32 is perfect & 2 is the 5th root).
is called perfect. Examples:
2. Index – The number that indicates how many times the root must be multiplied by itself to be perfect.
It is on the outside top left of the radical. If no index is indicated then 2 is assumed to be the index.
4  2 (since no index then 2 is the index so 2 multiplied by itself is 4),
8  2 (3 is the index so 2 multiplied by itself 3 times is 8),
5
32  2 (5 is the index so 2 multiplied by itself 5 times is 32).
Examples:
3
3. Root – This number multiplied by itself however many times indicated by the index is called the root
of the perfect radicand.
4. Radicand – Number under the radical symbol.
5. Simplifying Radicals – To simplify a radical try to rewrite the radicand in exponential form with a
base and an exponent that matches the index, if any exist, then take the root of the perfect radicand and
move the root out from under the radical and leave under the radical factors that are not perfect.
Examples: 4  22  2 ; 3 8  23  2 ; 4 48  4 24  3  2 4 3
6. Simplifying Radicals with Variables – Remember radicals with variables with exponents that match
the index are perfect. If you have a radical with a variable with an exponent, the
root of the radical is the variable with the exponent divided evenly by the index. If you have a radical
with a variable with an exponent, find the factors of the variable so that you have a variable product
that contains the exponent that matches the index. To do this just divide the exponent by the index and
then you have 2 factors one with an exponent matching the index and one with an exponent that does
not match the index. When simplified the radical is the root of the variable with the exponent with the
matching index multiplied by the radical with the variable with the exponent that does not match the
index.
3
Examples:
x 6  ( x3 )2  x3 ;
4
x 27  4 ( x 6 ) 4  x 3  x 6 4 x 3
B. Rules to Live by (Used for all indexes not just the index of 2) 1. Multiplication -
n
a  n b  n a b
n
2. Division -
a na

n
b
b
3. If x is any Real Number – When you take the Square Root - take the exponent, divide by 2 –
if even then  x n
if odd = x n this will take care of x if it is negative.
4. You can only Add or Subtract LIKE Radicals (under the radical has to be identical!).
5. NO Radicals can be left in the Denominator!
6. Rationalizing the Denominator - HINT: Simplify before you start rationalizing.
If you have one term in the denominator –
Multiply the numerator and the denominator by the multiple of 1 that
a
represents
a
denominator index-exponent
denominator index-exponent
and then simplify.
Where “a” represents the index.
If you have a binomial in the denominator –
Multiply the numerator and the denominator by the multiple of 1 that
represents
conjugate
and then simplify.
conjugate
WHRHS
2011-2012
Unit 6 - Radicals
Algebra 2A
Practice Problems:
1.
16
2.
32
3.
9.
x2
10.
ax 2
x3 y 5
.04
4.
3
81
11.
5.
4
243
12.
6.
3
96
13.  2 5 32 x 5 y 8
7.
4
96
3
a 2  4a  4
14.
8.
5
x6
96
15.
3
x 
16.
5
 r10 y 6
6
2
WHRHS
2011-2012
Unit 6 Day B HW – Simplifying Radical Expressions
1.
Unit 6 - Radicals
Algebra 2A
17. 4 x 5  x5 y 8
8
18.
2.
6
64 x 20 y17 z18
18
19. 2ab 50a 2b 4
3.
45
4.
20.
x 2  10 x  25
21.
5a 2  40a  80
200
5.
48
6.
288
7.
242
8.
3
9.
3
128
40
10.
3
11.
4
12.
3
432
1250
22.
4
162
23.
5
96
24.
5
480
25.
4
80
26.
5
2430
27.
3
x6
16m
9 x2 y 4
28.
13.
14.
4
4
25 x 5 y 2
29.
3
1015
30.
5
32
162 x 4 y11
15.  3 3 16 x 2 y 3
16.  200 xy 2 z 3
31.
50
32.
8x2