Powers and Radicals without Calculators (6.5)

Slides:

Advertisements

Similar presentations

How do we handle fractional exponents?

Advertisements

MTH 092 Section 15.1 Introduction to Radicals Section 15.2 Simplifying Radicals.

Section 6.2. Example 1: Simplify each Rational Exponent Step 1: Rewrite each radical in exponential form Step 2: Simplify using exponential properties.

9.3 Simplifying Radicals.

Objectives The student will be able to:

7. Roots and Radical Expressions

6-4: n th Roots I can simplify radicals and approximate them using a calculator.

Rewrite With Fractional Exponents. Rewrite with fractional exponent:

Fractional Exponents and Radicals

Topic: Simplifying Radical Expressions.  Product Property of Roots  The nth root of a product is equal to the product of the nth roots.  Ex.  We’ve.

Aim: Rational Exponents Course: Adv. Alg. & Trig. Aim: How do we handle fractional exponents? Do Now: 2 8 = 2 ? = 2 6 = 2 ? = 2 2 = 2 1 = 2 ? =

Real Numbers Real Numbers are all numbers that can be located on Real Number line. This includes all whole numbers, all fractions, all decimals, all roots,

Roots Rational Numbers Scientific Notation More with Exponents Laws of Exponents

6.1 n th Roots and Rational Exponents What you should learn: Goal1 Goal2 Evaluate nth roots of real numbers using both radical notation and rational exponent.

Working With Radicals. Do Now Simplify each of the exponential expressions.

Warm Up Simplify (10²)³

Cubes and Cube Roots 8th grade math.

Objective: Add, subtract and multiplying radical expressions; re-write rational exponents in radical form. Essential Question: What rules apply for adding,

 Form of notation for writing repeated multiplication using exponents.

9.2 Students will be able to use properties of radicals to simplify radicals. Warm-Up  Practice Page 507 – 508 l 41, 42, 45, 46, 55, 57, 59, 65.

Algebraic Expressions - Rules for Radicals Let’s review some concepts from Algebra 1. If you have the same index, you can rewrite division of radical expressions.

Exponents. Definition: Exponent The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to.

7.1 Radical Expressions.

Sums and Differences of Rational Expressions Putting factoring skills to use again (7.8)

Rational Exponents MATH 017 Intermediate Algebra S. Rook.

You should know or start to recognize these: 2 2 = 43 2 = 94 2 = = = 83 3 = = = = = = = = 323.

7-1 Zero and Negative Exponents

Exponents 8 th Grade Pre-Algebra. Real Numbers Rational Numbers: Any number that can be written as a fraction Integers Positive and negative whole numbers.

Fractions and Exponents  Step 1:  Understand the exponent means the number of times to multiply the “base” that it is on  Step 2:  Multiply  Step.

10/29/12 Unit 2Triangles Right Triangles I can….. simplify radical expressions.

Radicals without Calculators

Simplifying Radicals Definitely radical, debatably simple.

Not all numbers or expressions have an exact square or cube root. If a number is NOT a perfect square or cube, you might be able to simplify it. Simplifying.

Lesson 8-6B Use Cube Roots and Fractional Exponents After today’s lesson, you should be able to evaluate cube roots and simplify expressions with fractional.

Objective Students will add, subtract, multiply, divide, and simplify radicals.

Simplifying Radical Expressions

11-1 Simplifying Radicals

Exponents and Radicals Objective: To review rules and properties of exponents and radicals.

Algebraic Fractions. 1. Find the prime factorization of the following numbers. (Make a factor tree if necessary)  45  54  36  96  100  144.

Taking the n th Root to Solve Equations Chapter 7.1.

Complex Numbers Add and Subtract complex numbers Multiply and divide complex numbers.

Warm-up Write as a rational exponent. Answers:. Notes P3, Day 3: Cube Roots and Rational Exponents Definition of the Principal nth Root of a Real Number.

Properties and Rules for Exponents Properties and Rules for Radicals

6.2A – Solving Exponential Equations and Inequalities

6.1 Laws of Exponents.

Rational Exponents. Rational Exponent  “Rational” relates to fractions  Rational exponents mean having a fraction as an exponent. Each part of the fraction.

Fractional Exponents. Careful! Calculate the following in your calculator: 2 ^ ( 1 ÷ 2 ) Not Exact.

Warm Up:. 5.1 Notes: nth Roots and Rational Exponents.

Rational (fraction) exponents 6.4 We’ve worked with positive and negative exponents-- now, let’s move to fractions.

Minds On Unit 7: Exponential Functions The answer to a power is 9. What might the power be?

A radical equation is an equation that contains a radical. BACK.

Rewrite With Fractional Exponents. Rewrite with fractional exponent:

11.3 Solving Radical Equations Definitions & Rules Simplifying Radicals Practice Problems.

Objective: To simplify square roots and radical expressions. Standard 2.0.

Basic Algebra 1 Chapter 8 Powers and Roots. 8-5 Square Roots WARMUP Express in Scientific Notation: 1. 1,650,000, Evaluate: 1. (1.5 X 10.

8.6 Natural Logarithms.

Chapter R Section 7: Radical Notation and Rational Exponents

Unit 2 Day 7. Do now Simplify the square roots

Simplifying Radical Expressions (10-2)

Simplifying Radical Expressions

Day 102 – Performing Operations with Radicals

How would we simplify this expression?

If x2 = y then x is a square root of y.

1.4 Rational Exponents.

Section 7.2 Rational Exponents

9.3 Simplifying Radicals. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number a.

Simplify: (3xy4)(-2x2y2) x3y6 xy2 -6x3y6

Unit 1 Day 3 Rational Exponents

Presentation transcript:

Powers and Radicals without Calculators (6.5) Using a factor tree when your calculator goes on the fritz

A little review Let’s look again at yesterday’s exponential problems we simplified: (6x5)(3x-2) (5x-4)(2x-3) (-2x2)3(3x-1y2)4 (x-1y-4z)/(x-2yz-3) (3x-1/2)(4x2/3) (3758x89)(3758x-89) (u3.7p4.8)/(u-2.9p1.8)

A POD warm-up Rewrite each of the following using a radical sign: 81/3 2431/5 Can you figure out what they equal without using a calculator?

Let’s look more closely 81/3 What is the factor tree for 8? How could we use that to find the final answer?

Let’s look again more closely 2431/5 What is the factor tree for 243? How can we use it to find a final answer?

Now try this Use a factor tree to find 2561/4. Use it to find 641/3.

Let’s mix it up a bit What is 2431/5? What would 2433/5 equal then?

You design one Write a power expression with a fraction exponent that equals 2. We’ve seen that 81/3 will do this. Any others? How about one that equals 4?

Signs -2431/5 equals -3 2561/4 equals 4 641/3 equals 4 So, we can take: the even root of a positive number. the odd root of a positive number. the odd root of a negative number. But we cannot take: the even root of a negative number (remember finding the square root of a negative number?)