Download radicals – part 2

Simplifying Radical Expressions
Algebra 1
If b 2 = a, then b is a square root of a.
Meaning
Positive
Square Root

Symbol
Example
Negative
Square Root
9 3
 9  3
The positive and
negative square
roots

 9  3
Simplifying Radical Expressions
Product Property for Radicals
ab  a  b
36  4  9
100  4  25
36  4  9
10  2  5
6  23
Simplifying Radical Expressions
Product Property for Radicals
50  25  2
5 2
• A radical has been simplified when its
radicand contains no perfect square factors.
• Test to see if it can be divided by 4, then 9,
then 25, then 49, etc.
• Sometimes factoring the radicand using the
“tree” is helpful.
x x
14
7
Steps
1. Try to divide the radicand into a perfect
square for numbers
2. If there is an exponent make it even by
using rules of exponents
3. Separate the factors to its own square root
4. Simplify
Simplify:
45
9 5
3 5
Simplify:
49 x
49  x
7 x
Simplify:
52t
4  13t
2 13t
Simplify:
12
x
x 
2
6
x
6
Square root of a variable to an
even power = the variable to
one-half the power.
Simplify:
y
y
88
44
Square root of a variable to an
even power = the variable to
one-half the power.
Simplify:
x  x x
12 1
13
x  x
12
x
6
x
x
Simplify:
27
x  x
26
13
x
x
Simplify:
36x
8
6  x
2
6x
4
8
Simplify:
10
49 y
7y
5
Simplify:
45x
6
9x  5
6
3x
3
5
Simplify:
50 y
7
25 y  2 y
6
5y
3
2y
Simplify:
48y
9
Simplify:
80 y
16
16 y  5
16
4y
8
5
Simplify:
36x
3
6x x
4
448x y
Simplify:
7
4x y  112 y
4
2
2x y
3
6
 4  28y
2 x y  2  4  7y
2
3
2
8x y
3
7y
•
square root: one of two equal factors of a given number. The radicand is like the
“area” of a square and the simplified answer is the length of the side of the squares.
•
Principal square root: the positive square root of a number; the principal square
root of 9 is 3.
9 3
•
negative square root: the negative square root of 9 is –3 and is shown like
 9  3
•
radical: the symbol
which is read “the square root of a” is called a radical.
•
radicand: the number or expression inside a radical symbol
radicand.
•
perfect square: a number that is the square of an integer. 1, 4, 9, 16, 25, 36, etc…
are perfect squares.
•
irrational number: a number whose decimal form is nonterminating and
nonrepeating. 2
•
Rational number: a number that can be written in the form a/b, where a and b
are integers (b cannot equal 0)
•
radical expression: an expression that contains a radical.
3
--- 3 is the
25  4
 y  3
36
Simplify:
 y  3
18
Simplify:
2 x  20 x  50
2
2x  10 x  25
2
2
x  5
2  x  5
2
y  6y  9
2
Simplify:
 y  3
y 3
2
4  x  5
10
Simplify:
4
 x  5
2  x  5
10
5
50  y  7 
9
Simplify:
25  y  7   2  y  7 
8
5 y  7
4
2  y  7