Section 9.1 Finding Roots
OBJECTIVES Find the square root of a number. A Square a radical expression. B
OBJECTIVES Classify the square root of a number and approximate it with a calculator. C
OBJECTIVES Find higher roots of numbers. D Solve an application involving square roots. E
DEFINITION If a is a positive real number, Square Root
DEFINITION Square Root
When the square root of a non- negative real number a is squared, the result is that positive real number: RULE Squaring a Square Root
RULE Square Root of a Negative Number
Section 9.1 Exercise #1 Chapter 9 Roots and Radicals
Find.
Section 9.1 Exercise #2 Chapter 9 Roots and Radicals
Find the square of each radical expression.
Section 9.1 Exercise #3 Chapter 9 Roots and Radicals
Classify each number as rational, irrational, or not a real number, and simplify if possible.
Section 9.1 Exercise #4 Chapter 9 Roots and Radicals
Find each root, if possible.
Section 9.1 Exercise #5 Chapter 9 Roots and Radicals
The diver takes 2 seconds. A diver jumps from a cliff 20 meters high. If the time t (in seconds) it takes an object dropped from a distance d (in meters) to reach the ground is given by: How long does it take the diver to reach the water?
Section 9.2 Multiplication and Division of Radicals
OBJECTIVES Multiply and simplify radicals using the product rule. A
OBJECTIVES Divide and simplify radicals using the quotient rule. B
OBJECTIVES Simplify radicals involving variables. C
OBJECTIVES Simplify higher roots. D
If a and b are nonnegative numbers, Product Rule for Radicals
If a and b are positive numbers, Quotient Rule for Radicals
For any real number a, Absolute Value for Radicals
For all real numbers where the indicated roots exist, Properties of Radicals
Section 9.2 Exercise #6 Chapter 9 Roots and Radicals
Simplify.
Section 9.2 Exercise #7 Chapter 9 Roots and Radicals
Multiply.
Section 9.2 Exercise #8 Chapter 9 Roots and Radicals
Simplify.
Section 9.2 Exercise #9 Chapter 9 Roots and Radicals
Simplify.
Section 9.2 Exercise #10 Chapter 9 Roots and Radicals
Simplify.
Section 9.3 Addition and Subtractions of Radicals
OBJECTIVES Add and subtract like radicals. A
OBJECTIVES Use the distributive property to simplify radicals. B
OBJECTIVES Rationalize the denominator in an expression. C
Rationalizing Denominators PROCEDURE Method 1: Multiply both numerator and denominator of the fraction by the square root in the denominator.
Rationalizing Denominators PROCEDURE Method 2: Multiply numerator and denominator by the square root of a number that makes the denominator the square root of a perfect square.
Section 9.3 Exercise #11 Chapter 9 Roots and Radicals
Simplify.
Section 9.3 Exercise #12 Chapter 9 Roots and Radicals
Simplify.
Section 9.3 Exercise #13 Chapter 9 Roots and Radicals
Simplify.
Section 9.3 Exercise #14 Chapter 9 Roots and Radicals
Section 9.3 Exercise #15 Chapter 9 Roots and Radicals
Section 9.4 Simplifying Radicals
OBJECTIVES Simplify a radical expression involving products, quotients, sums, or differences. A
OBJECTIVES Use the conjugate of a number to rationalize the denominator of an expression. B
OBJECTIVES Reduce a fraction involving a radical by factoring. C
Simplifying Radical Expressions RULES 1. Whenever possible, write the rational-number representation of a radical expression.
Simplifying Radical Expressions RULES
Simplifying Radical Expressions RULES
Section 9.4 Exercise #16 Chapter 9 Roots and Radicals
Simplify.
Section 9.4 Exercise #17 Chapter 9 Roots and Radicals
Simplify.
Section 9.4 Exercise #18 Chapter 9 Roots and Radicals
Simplify.
Section 9.4 Exercise #19 Chapter 9 Roots and Radicals
Simplify.
Section 9.4 Exercise #20 Chapter 9 Roots and Radicals
Simplify.
Section 9.5 Applications
OBJECTIVES Solve equations with one square root term containing the variable. A
OBJECTIVES Solve equations with two square root terms containing the variable. B
OBJECTIVES Solve an application. C
Raising Both Sides of an Equation to a Power PROCEDURE
Solving Radical Equations PROCEDURE 1. Isolate the square root term containing the variable. 2. Square both sides of the equation.
Solving Radical Equations PROCEDURE 3. Simplify and repeat steps 1 and 2 if there is a square root term containing the variable.
Solving Radical Equations PROCEDURE 4. Solve the resulting linear or quadratic equation. 5. Check all proposed solutions in the original equation.
Section 9.5 Exercise #22 Chapter 9 Roots and Radicals
Solve.
Section 9.5 Exercise #23 Chapter 9 Roots and Radicals
Solve.
Section 9.5 Exercise #24 Chapter 9 Roots and Radicals
Solve.