Do Now 4/19/10 Copy HW in your planner. Copy HW in your planner. Text p. 655, #4-48 multiples of 4, #56 & 60 Text p. 655, #4-48 multiples of 4, #56 & 60.

Slides:

Advertisements

Similar presentations

Find Square Roots and Compare Real Numbers

Advertisements

solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.

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.

Introduction You can determine how far a ladder will extend from the base of a wall by creating a quadratic equation and then taking the square root. To.

Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.

Roots Lesson #8 Pg Simplify each expression. 1) 6² 36 2) ) (–9)(–9) 81 4) Write each fraction as a decimal. 5) ) 7) 5.

Section 7.1 Extraction of Roots and Properties of Square Roots.

Questions from HW??? Use Square Roots to Solve Quadratic Equations Test: FRIDAY!!!!

Sections 11.1: Square Roots & 11.2: Approximating Square Roots Pg.533, 540.

Solving Quadratic Equations by Completing the Square

Do Now: Solve the following equations: x 2 = 25 x 2 = 50 Explain your thinking.

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,

or –5 The side length of a square is the square root of its area.

Introduction The properties of integer exponents also apply to irrational exponents. In this section, we will see how the following properties can be used.

Rational and Irrational Numbers

1.3 – Real Numbers and the Number Line. I.SQUARES and SQUARE ROOTS: The term square root comes from the AREAS of squares and their sides. Because 9 =

Do Now 1/12/10 Copy HW in your planner. –Text p. 222, #20-60 evens Open your notebook to a new page and put the following heading on the top of the page.

The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all.

Lesson 11-1 Warm-Up. Lesson 11-1 Warm-Up Square Roots and Irrational Numbers (11-1) What is a “perfect square”? What is a “square root”?? perfect square:

Algebra 1 Chapter 1 Section 5.

Square Roots Tutorial 12c Introduction to Square Roots Just as the inverse of addition is subtraction, and of multiplication is division, the inverse.

Find the Square Root: 1) 3) 2) 4)

Do Now 9/24/09 Take out your HW from last night. Take out your HW from last night. Text p , #14-24 even, #32-50 even Text p , #14-24 even,

6:12-4 Exploring square roots and rational numbers.

2.13 Warm Up x² - 2x + 15 = 0; 3 x² + 3x – 4 = 0; 1

Unit 2 Solving Polynomials by Taking the Square Root.

Quadratic Formula Standard Form of a Quadratic Equation ax 2 + bx + c = 0  example  x 2 + 6x + 8 = 0  we learned to solve this by:  factoring  completing.

2.13 Use Square Roots to Solve Quadratics Example 1 Solve quadratic equations Solution Write original equation. 5 Solve the equation. Add __ to each side.

Goal: Solving quadratic equations by finding square roots.

The Real Number System Real Numbers Irrational Numbers

Do Now 3/2/11 Take out HW from last night. –Text p. 222, #1-4 all, all, evens, evens Copy HW in your planner. –Text p. 222, #28-35 all,

Section 2-8 Definitions Square root: = 6. Radical sign: This is a radical sign. Perfect square: 4, 9, 16, 25, … are perfect square numbers. Because 2*2=4,

Chapter 1: Real Numbers and Equations Section 1.1: The Set of Real Numbers.

Do Now 5/4/10 Take out HW from last night. Take out HW from last night. Cumulative Test Chapters 1-10 Cumulative Test Chapters 1-10 Copy HW in your planner.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1 Chapter 9 Quadratic Equations and Functions.

Opener-SAME SHEET-12/6 Find each square root. Solve each equation.

Do Now 2/1/10 Take out HW from Friday Take out HW from Friday Text p. 258, #8-40 evens, & 11 Text p. 258, #8-40 evens, & 11 Copy HW in your planner. Copy.

Do Now 4/28/11 Take out HW from last Wednesday. Take out HW from last Wednesday. Text p. 337, #10-22 even, & #26 Text p. 337, #10-22 even, & #26 Copy HW.

9.1 – Finding Square Roots. We know how to find the square of a number: 3 2 = (-3) 2 =

Do Now 9/23/ A= 16 A = 4² A= 36 A = 6² 4 What is the area for each figure? What are the dimensions for each figure? Write an equation for area of.

Warm Up Find each quotient / divided by 3/5

9.1 Solving Quadratic Equations by Finding Square Roots.

Do Now 3/1/11 Copy HW in your planner. –Text p. 222, #1-4 all, all, evens, evens Open your notebook to a new page and put the following.

Standard 8 Solve a quadratic equation Solve 6(x – 4) 2 = 42. Round the solutions to the nearest hundredth. 6(x – 4) 2 = 42 Write original equation. (x.

Solving Quadratic Equations by Using the Quadratic Formula (9-5) Objective: Solve quadratic equations by using the Quadratic Formula. Use the discriminant.

1-2 Irrational Numbers and Square Roots. Video Tutor Help Irrational Numbers Classifying Real Numbers Khan Academy Word Problem: given area find side.

Square Roots. Perfect Squares Squaring is when a number is multiplied by itself – It’s called squared because the area of a square is multiplying a side.

Section 5-4 The Irrational Numbers Objectives: Define irrational numbers Simplify radicals Add, subtract, multiply, and divide square roots Rationalize.

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.

Square Roots All positive real numbers have two square roots, a positive and negative square root. All positive real numbers have two square roots, a positive.

Module XIII, Lesson 3 Online Algebra

11.1 and 11.2 Radicals List all the perfect squares:

9.1 Solving quadratic equations using square roots

The Quadratic Formula..

(as opposed to fake numbers?)

(as opposed to fake numbers?)

Warm-Up #12 (Monday, 9/28) 3 ∙ ∙ (2 5 − 125)

§5.4, Irrational Numbers.

Solving Quadratic Equations using Square Roots

(as opposed to fake numbers?)

(as opposed to fake numbers?)

10.5 Use Square Roots to Solve Quadratic Equations

The Real Number System Real Numbers Irrational Numbers

9.2 Solving Quadratic Equations using square roots

Introduction You can determine how far a ladder will extend from the base of a wall by creating a quadratic equation and then taking the square root. To.

Do Now 4/29/19 Take out CW/HW from last week. Practice worksheet 9.1

Section 9.1 “Properties of Radicals”

(as opposed to fake numbers?)

Presentation transcript:

Do Now 4/19/10 Copy HW in your planner. Copy HW in your planner. Text p. 655, #4-48 multiples of 4, #56 & 60 Text p. 655, #4-48 multiples of 4, #56 & A= 16 A = 4² A= 36 A = 6² 4 What is the area for each figure? What are the dimensions for each figure? Write an equation for area of the figure? Can you think of an equation for ONE side of the figure?

Objective SWBAT solve quadratic equations by finding square roots SWBAT solve quadratic equations by finding square roots

Remember This??? Section 2.7 “Find Square Roots and Compare Numbers” If b² = a then b is the square root of a. The SQUARE ROOT of a number is denoted by the symbol, which is called a radical. radicand

Square Roots All positive real numbers have two square roots, a positive and negative square root. All positive real numbers have two square roots, a positive and negative square root. The symbol is read as “plus or minus” and refers to both the positive and negative square root. The symbol is read as “plus or minus” and refers to both the positive and negative square root. Negative real numbers do not have real square roots. So there is no solution. Negative real numbers do not have real square roots. So there is no solution. perfect square The square of an integer is called a perfect square. no solution

Not PERFECT??? The square root of a whole number that is NOT a perfect square is an IRRATIONAL NUMBER. numbers that cannot be written as a quotient (fraction, ratio) of two integers and the decimal neither terminates nor repeats. To find the square root of a number that is not a perfect square estimate or use a calculator to find the square root.

Section 10.4 “Use Square Roots to Solve Quadratic Equations” To use square roots to solve a quadratic equation of the form ax² + bx + c = 0, first isolate x² on one side of the equation to obtain x² = d. To use square roots to solve a quadratic equation of the form ax² + bx + c = 0, first isolate x² on one side of the equation to obtain x² = d. x² = d Solving x² = d by Taking Square Roots - If d > 0, then x² = d has two solutions: - If d = 0, then x² = d has one solution: - If d < 0, then x² = d has no solution: no solution Examples

Try It Out… No solution

Take square roots of a fraction In cases where you need to take the square root of a fraction whose numerator and denominator are perfect squares, the radical can be written as a fraction. In cases where you need to take the square root of a fraction whose numerator and denominator are perfect squares, the radical can be written as a fraction. For example, can be written as. For example, can be written as.

Try It Out…

Solve the quadratic equation. Round your answer to the nearest hundredth.

Homework Text p. 655, #4-48 multiples of 4, #56 & 60