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Simplifying Radical Expressions

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Presentation on theme: "Simplifying Radical Expressions"— Presentation transcript:

1 Simplifying Radical Expressions

2 Product Property of Radicals
For any numbers a and b where and ,

3 Product Property of Radicals Examples

4 Examples:

5 Examples:

6 Quotient Property of Radicals
For any numbers a and b where and ,

7 Examples:

8 Examples:

9 Rationalizing the denominator
Rationalizing the denominator means to remove any radicals from the denominator. Ex: Simplify

10 Simplest Radical Form No perfect nth power factors other than 1.
No fractions in the radicand. No radicals in the denominator.

11 Examples:

12 Examples:

13 Reverse of the Distributive Property
Adding radicals We can only combine terms with radicals if we have like radicals Reverse of the Distributive Property

14 Examples:

15 Examples:

16 Multiplying radicals - Distributive Property

17 Multiplying radicals - Distributive

18 Examples:

19 Examples:

20 where a, b, c, d are rational numbers.
Conjugates Binomials of the form where a, b, c, d are rational numbers.

21 The product of conjugates is a rational number
The product of conjugates is a rational number. Therefore, we can rationalize denominator of a fraction by multiplying by its conjugate.

22 Examples:

23 Examples:


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