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Real Numbers

Radicals

Inequalities & Absolute Value

Polynomials

Rational Expressions 1

Rat'l. Exp. 2 - mult&div

Rat'l. Exp. 3 - add&subt

Slope & Equations of Lines

Review&Test

 

 

jdsmathnotes

 


 

 UNIT 1 : PRECALCULUS PREP

 LESSON 2: REAL NUMBERS - RADICALS

 

Examples Of Radicals:

 

 

NOTE: Each of these examples is an irrational real number.

 

Properties of Radicals:

 

Text Box:

 

 

 

 

 

 

 

Example 1:

 

Mixed and Entire Radicals:

 

Example 2: Write as mixed radicals.

 

Solutions:

 

 

 

 

 

Text Box: Tips for Changing to Mixed Radicals:
	Break the radical into two factors
	Use the following set of perfect squares to get the first factor 
	{4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, }
	Take the square root of the first number to get the first factor of the mixed radical.
 


 

 

 

 

 

 

 

 

Example 3: Write as entire radicals.

 

Solutions:

 

 

 

 

Multiplying Radicals:

Example 4: Simplify

 

 

 

Solutions:

 

 

 

 

Addition and Subtraction of Radicals:

Radicals are added/subtracted just as in ordinary algebra using LIKE TERMS.

Examples:

2x 3y + 5x 6y = 2x + 5x 3y 6y = 7x 9y

Similarly

 

Example 5: Simplify

Solutions:

 

 

Example 6: Simplify

 

Solutions:

Again we follow the rules of ordinary algebra for expanding

 

Recall from ordinary algebra the product of two binomials:

(x + 3)(x + 5) = x(x + 5) + 3(x + 5)

= x2 + 5x + 3x + 15

= x2 + 8x + 15

 

 

 

 

Division of Radicals:

 

Recall all of the properties of radicals mentioned above:

 

Text Box:

 

 

 

 

 

 

 

 

Example 7: Simplify

 

Division of Radicals with Irrational denominators: Examples:

 

These are simplified by a process called rationalizing the denominator.

 

Example 8: Simplify by rationalizing the denominator.

 

Example 9: Simplify

Example 10: Simplify

Example 11: Simplify


 

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