Transcript Lesson 3.4 Simplify Radical Expressions

Simplify Radical
Expressions
EQs…
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How do we simplify algebraic and numeric
expressions involving square root?
How do we perform operations with square
roots?
Vocabulary
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Simplest Form – A radical expression is in
simplest form if no perfect square factors
other than 1 are in the radicand, no
fractions are in the radicand, and no
radicals appear in the denominator of the
fraction.
Rationalizing the Denominator – The
process of eliminating a radical from an
expression’s denominator.
Vocabulary
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Radical Conjugates – a  b and a  b
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Product Property of Radicals – States that the
square root of a product equals the product of
the square roots of the factors.
ab  a  b where a  0 and b  0
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Quotient Property of Radicals – States that the
square roots of a quotient equals the quotient of
the square roots of the numerator and
denominator. a
a

where a  0 and b  0
b
b
Example 1
Use the product property of radicals
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Simplify the expression.
28
50 y
3
Example 2
Multiply radicals
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Simplify the expression.
2  18
5 2 xy  32 y
Example 3
Use the quotient property of radicals
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Simplify the expression.
17
25
4
2
49 y
Guided Practice for Examples 1, 2, & 3
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Simplify the expression.
1. 72
2. 3 x 2
3. 45 y
5
4. 3 12x
2
Guided Practice for Examples 1, 2, & 3
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Simplify the expression.
5. 5  10
6. 3 x  15xy
7.
5
81
8.
2x2
9 y2
Example 4
Rationalize the denominator
3
6x
1
3 2
Example 5
Add and Subtract Radicals
3 3  6 27
11 5  2 20
Guided Practice for Examples 4 & 5
Add and Subtract Radicals
3
9.
2x
10. 6 7  8 10  3 7
11. 3 5  2 500
Joke of the Day…
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Why was the math book crying?
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It had too many problems!