simplifying radical expressions algebra 1 if b 2 = a, then b is a square root of a. meaningpositive...
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Simplifying Radical Expressions
Algebra 1
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If b 2 = a, then b is a square root of a.
Meaning Positive
Square Root
Negative
Square Root
The positive and negative square
roots
Symbol
Example
39 39 39
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Simplifying Radical Expressions
100 4 25 36 4 9
326
Product Property for Radicals
ab a b
10 2 5 36 4 9
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Simplifying Radical Expressions
• 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.
Product Property for Radicals
50 25 2 5 2
14 7x x
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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
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Simplify: 45
59
53
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Simplify: x49
x49
x7
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Simplify: t52
t134
t132
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Simplify:12x
6x
26x
Square root of a variable to an even power = the
variable to one-half the power.
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Simplify:88y
44y
Square root of a variable to an even power = the
variable to one-half the power.
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Simplify:13x
xx6
12x x
112xx
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Simplify:27x
13x x
26x x
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Simplify:836x
46x
2 86 x
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Simplify:1049y
57 y
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Simplify:645x
33 5x
69 5x
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Simplify:750y
35 2y y
625 2y y
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Simplify:948y
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Simplify:1680y
84 5y
1616 5y
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Simplify:336x
6x x
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Simplify:4 7448x y
2 38 7x y y
4 6 1124x y y
2 32x y 4 28y
2 32 2x y 4 7 y
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• 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.
• negative square root: the negative square root of 9 is –3 and is shown like
• radical: the symbol which is read “the square root of a” is called a radical.
• radicand: the number or expression inside a radical symbol --- 3 is the 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.
• 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.
39
39
3
2
25 4
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Simplify: 363y
183y
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Simplify: 50202 2 xx
52 x
25102 2 xx
252 x
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Simplify:2 6 9y y
3y
23y
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Simplify: 104 5x
52 5x
104 5x
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Simplify: 950 7y
45 7 2 7y y
825 7 2 7y y