Transcript 20_01 - Simplifying Radicals

1)
x2 + x – 30 = 0
Solve:
( x + 6 )( x – 5 ) = 0
x+6 = 0
or
x–5= 0
x = –6
2)
x = 5
x2 + 9x = 0
Solve:
x( x + 9 ) = 0
x = 0
x = 0
or
x+9 = 0
x = –9
20.01
Simplifying
Radicals
A perfect square is a number that results
from squaring the counting numbers.
When you square a number, it is
raised to the second power.
12 = 1 , 22 = 4 , 32 = 9 , 42 = 16 ,
52 = 25 , 62 = 36 , 72 = 49 , …
Perfect Squares: 1 , 4 , 9 , 16 , 25 , 36 ,
49 , 64 , 81 , 100 , …
A Square Root Symbol
is called a square root or radical symbol.
x
means “ the square root of x”
or “radical x”
By definition:
x
=k
such that k2 = x
36 = 6 because 62 = 36
64 = 8 because 82 = 64
Some radicals will not simplify to a whole number.
When this happens, we still may
be able to simplify the radical.
To simplify a radical, rewrite the radical as a product
of its largest perfect square factor and the remaining
factor. Simplify the perfect square radical and leave
the other radical alone.
x  a b
where a is the largest square factor of x
x 
a
b
1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , …
Simplify the following radicals.
12 
4
3
2 3
45 
9
5
3 5
98 
49 
2 7 2
x 
Try This:
a
b
1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , …
Simplify the following radicals.
50 
25 
2
5 2
48 
16 
3
4 3
500 
72

100 
36 
5  10 5
2
6 2