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