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

Slides:

Advertisements

Similar presentations

Advertisements

Aim: How do we simplify radical expressions? Do Now: List at least 3 factors of: x 4.

Examples for Rationalizing the Denominator Examples It is improper for a fraction to have a radical in its denominator. To remove the radical we “rationalize.

7. Roots and Radical Expressions

6-5: Operations with Radical Expressions I can add or subtract expressions involving radicals.

EXAMPLE 1 Solve quadratic equations Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ±

11.1 and 11.2 Radicals Goal(s): 1.To find the square roots of perfect squares, perfect square radicands and estimate the roots of irrational numbers 2.Determine.

= 9 = 8 = 12 = 19 = 2 = 3 = 17 = 5 = 11 = 5.

9-1 Square Roots Find the square root for each. 1.) 25 2.) 49 The square root sign is also called a radical. The radical sign represents a nonnegative.

People Fractions. Problem 1 of 20 Answer 1 = 10 Problem 2 of 20 Answer 2 = 5.

Powers and Radicals without Calculators (6.5)

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.

6.1 Radical Expression Function and Models. Properties of Square Roots Every positive real number has two real-number square roots. The number 0 has just.

11.1 Examples for Division (EX: 1 of 4) Next Example Break the fraction up…move the radical sign to both the numerator and the denominator Can you divide?

Unit 2 Solving Polynomials by Taking the Square Root.

Imaginary & Complex Numbers Obj: Simplify expressions with imaginary numbers; re-write radicals as complex expressions. Why do imaginary numbers exists.

Roots of Real Numbers.

Bell Ringer Use the Pythagorean Theorem to find the length of the hypotenuse.

Exponents and Powers Power – the result of raising a base to an exponent. Ex. 32 Base – the number being raised to the exponent. Ex is the base.

Simplifying Radicals Definitely radical, debatably simple.

Write the radical expression in simplest form.

( + ) ÷ ( + ) = ( + ) ( – ) ÷ ( – ) = ( + ) Simplify the following. ( + ) ÷ ( – ) = ( – ) ( – ) ÷ ( + ) = ( – ) 1) – 54 ÷ ( – 9 )= 6 2) – 48 ÷ 6= – 8 3)

Lesson 7-1: Radical Expressions Objectives Students will: Find square roots of numbers Find n-th root of numbers.

Cube Roots a is a cube root of b if and only if Example 1 2 is a cube root of 8, since - 2 is a cube root of - 8, since.

To simplify radicals: look for a square factor or a pair of factors.

Simplifying Radicals Section 5.3. Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator.

5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.

Radical Basics We will work with square roots, thus, you do not need to write the index. The index for square roots is 2.

Chapter 10.5 Notes Part I: Simplify Radical Expressions Goal: You will simplify radical expressions.

5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study.

Simplified Radical Form Objective: 1)Describe simplified Radical Form 2)Simplify radical expressions by a) Factoring out perfect squares b) Combine Like.

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.

Warm Up Find each quotient / divided by 3/5

Square Roots Unit 1D Day 17. Do Now What are the factors of x ² + 2 x – 3? Solve for x : x ² + 2 x – 3 = 0 What are the x -intercepts of y = x ² + 2 x.

Advanced Algebra Notes Section 4.5: Simplifying Radicals (A) A number r is a _____________ of a number x if. The number r is a factor that is used twice.

5.5 Factoring Special Patterns 11/20/2013. Perfect Squares

Absolute Value Absolute Value is the distance a number is away from zero on the number line. Find.| 4 | 4 | – 4 | 4 * Absolute Value Is ALWAYS POSITIVE!!!!*

No perfect square factors other than 1 are in the radicand. No fractions are in the radicand. No radicals appear in the denominator.

Lesson 1 MI/Vocab radical expression radicand rationalizing the denominator conjugate Simplify radical expression using the Product Property of Square.

Rewrite With Fractional Exponents. Rewrite with fractional exponent:

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

 A radical expression is an expression with a square root  A radicand is the expression under the square root sign  We can NEVER have a radical in the.

Algebra 1 Section 9.1 Evaluate square roots Solve simple quadratic equations Note: 5 2 = 25 and (-5) 2 = 25 so both 5 and -5 are square roots of 25. What.

5-5 Roots of Real Numbers II

Introduction to Square Roots

Simplifying Radical Expressions (10-2)

Objectives The student will be able to:

11.1 and 11.2 Radicals List all the perfect squares:

Simplifying Radical Expressions

Don’t be squared – get started!

Lesson 9.1: Radicals (Square roots)

Review Problems Algebra 1 11-R.

Simplifying Radicals.

Perfect Squares & Square Roots

7. Roots and Radical Expressions

Objectives The student will be able to:

Success Criteria LT: Today’s Agenda Do Now Hand Back Test Lesson HW#9

Must Do (8/29) – (-7) 8 – 12 (-7) + (-4)

No calculators allowed

75 Practice Ex 1: Ex 2: Rationalizing the Denominator Ex 1: Ex 2:

Squaring a value and finding its square root is the opposite

Simplifying Square Roots

10.1 Square Roots Objective: students will learn about square roots and how to use them to evaluate problems.

Work out (if you can, simplify your answer) 8 6.

Section 7.2 Rational Exponents

Rationalize Non-Perfect Squares

10-1 Simplifying Radicals

Unit 1.3 Part A Learning Goal:

Dividing Radical Expressions

GSE Algebra I Today’s Question: How do we simplify square roots?

Presentation transcript:

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

A “radical” or “square root sign” means the power is a fraction

Absolute Value

Ex:

HW: all

Answer Key: Evens 12. ±11x 2 y ±7x a 8 b 10 c (x + 15) (a 2 + 4a) d 4 x |(2x + 1) 3 | 26. –(y – 9) |a 3 | 30. 3|(x + 4)| 32. (y 3 + 5)6 34. x 2 |y| ±8iy 4 z ±2x 4 y cd –(y – z) 3