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7.1 and 7.2 Simplifying/Multiplying/Dividing Radical expressions

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## 7.1 and 7.2 Simplifying/Multiplying/Dividing Radical expressions

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**7.1 and 7.2 Simplifying/Multiplying/Dividing Radical**expressions**For any real number a and b, and any positive integer n, if**an = b , then a is the nth root of b.**Real Number Examples:**Find the roots: • Square Root of 4 Square Root of -4 • Cube Root of 8 Cube Root of -8 • Fourth Root of 16 Fourth Root of -16 • Fifth Root of 32 Fifth Root of -32**Variable Examples:**Find the Square Root of: • a1 2. a2 3. a3 4. a4**When a number has two real roots, the positive root is**called the principal root. • We always use the principal root when simplifying.**Examples – Simplify :**1. 2.**7.**8. 9.**10.**11. 12.**Multiplying and Dividing Radical Expressions**• If they are real numbers, then**Examples:**1. 2.**3.**4.**5.**6.**Examples:**1. 2.**Rationalizing the Denominator****Multiply the numerator and denominator by the denominator** Then Simplify Example: 1.**2.**3.**4.**5.**7.3Adding, Subtracting, Multiplying and Dividing Binomial**Radical Expressions**Adding Radical Expressions**• Use the same concept as that of adding or subtracting like variables. • Example: 7 - 3x + 2x + 5 *Have to have like Terms to Add/Subtract***Like Radicals are radical expressions that have the same**index and the same radicand.**Examples:**1. 2.**3.**4. 5. 6.**3.**4. 5. 6.**Multiplying Radical Expressions**When multiplying radicals, one must multiply the numbers OUTSIDE (O) the radicals AND then multiply the numbers INSIDE (I) the radicals.**Dividing Radical Expressions**When dividing radicals, one must divide the numbers OUTSIDE (O) the radicals AND then divide the numbers INSIDE (I) the radicals. Remember to rationalize the denominator if needed!**Examples:**1. 2.**Multiplying Binomials**To multiply, USE FOIL! Example 1:**Dividing Binomial Radicals**To divide, Rationalize the denominator! (a + b)( a - b) = a2 – b2 These are called conjugates! They make radicals disappear!**Examples:**1.**Solve:**1. 2.**3.**4.**Examples:**1.**Homework**Practice: Practice 7-3 #1-30 Left Column