And Squares Square Roots. If a square measures 4 inches on each side, how would you find its area? 4 inches.

Slides:



Advertisements
Similar presentations
KS3 Mathematics N4 Powers and roots
Advertisements

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.
Bell Ringer.
4.6-Square Roots and the Pythagorean Theorem CATHERINE CONWAY MATH081.
Algebra 9.1 Square Roots I will use the inverse of perfect squares to find approximate values of square roots. I will use square roots to evaluate radical.
What does it mean when we see numbers written like this: 4²10² 9² Since our exponent is 2, it means that we multiply the number by itself! So we have.
Rational and Irrational Numbers
Objectives The student will be able to simplify a cube root. SOL: A
Numerical Roots & Radicals
Square and Cube Roots Roots and Radicals Mr. O.
Squares and square roots
Square Roots and the Pythagorean Theorem Section 6.4.
Evaluating Square Roots
Tidewater Community College
Find the area of each square. How do you find the area of each square? Area may be found by either counting the number of units or multiply length of.
Algebra Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.
Find square roots. Find cube roots. 7.1 Objective The student will be able to:
Perfect Numbers- Squares and Cubes
Exponents and Squares Numbers and Operations. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being.
Students will be able to estimate a square root, simplify a square root, and add and multiply square roots.
Roots and Radicals. Radicals (also called roots) are directly related to exponents.
Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.
9.1 To evaluate square roots Objective Part I Evaluating Square Roots
Math 009 Unit 4 Lesson 4.
Algebra 2: Unit 8 Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.
Lesson 10-3 Warm-Up.
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.
Squares and Square Roots. Vocabulary Square root- A number that when multiplied by itself forms a product. Principal square root- the nonnegative square.
Chapter 8 Section 1. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Evaluating Roots Find square roots. Decide whether a given root.
Radicals Tammy Wallace Varina High. Perfect Squares A number is a perfect square if it is the product of a number and itself. The first 12 perfect squares:
Powers and Exponents. A power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent,
Algebra Foundations Perfect Square Mrs. Triechler.
Squares, Square Roots and Perfect Squares
Squares & Square Roots. Squares 3 We say, “Three squared is 9. We write 3 X 3 = 9 The square of three means a Square with three units on each side. There.
Definitions: Exponent – Is the number that tells us how many times to multiply a number (called the base) by itself. Base – Is a number that is multiplied.
Cubes and Cube Roots Wednesday, February 25 th. Objective The student will be able to simplify a cube root.
8-7 Powers and Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
UNIT 4- radicals simplify a cube root and higher.
Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.
And Squares Square Roots. If a square measures 4 inches on each side, how would you find its area? 4 inches.
Copyright © Cengage Learning. All rights reserved. Functions 1 Basic Concepts.
Quadratic Equation U n i t Solving by taking the Square Root Medina 1.
1 Chapter Chapter 2 The Whole Numbers.
Real Numbers and the Number Line
Write each fraction as a decimal.
Quadratic Equation Unit
Chapter 8 Section 1.
The student will be able to
Squares and Square Roots
1.2 Square Roots of Non-Perfect Squares
CUBE ROOTS.
Math 009 Unit 4 Lesson 4.
Write each fraction as a decimal.
Math 009 Unit 4 Lesson 4.
Section 5.4 The Irrational Numbers and the Real Number System
Section 5.4 The Irrational Numbers and the Real Number System
The number inside the radical symbol
Math 009 Unit 4 Lesson 4.
Powers and Exponents, Square Roots
Radicals (also called roots) are directly related to exponents.
Squares and square roots
Square and Cube Roots Roots and Radicals.
Exponents.
Pre-Algebra Roots and Radicals.
The student will be able to
Square Roots and Cubes Roots of Whole Numbers
Square Roots and Real Numbers
Activator Using the cubes in front of you build the following square shapes: 2 by 2, 3 by 3, and 4 by 4 How many blocks were in each square shape? What.
Write each fraction as a decimal.
Warm Up Simplify
Presentation transcript:

and Squares Square Roots

If a square measures 4 inches on each side, how would you find its area? 4 inches

We will: Understand the meaning of squaring a number and finding the square root of a number Find squares of numbers Raise a whole number to a whole number power Find square roots of perfect squares Find approximate square roots of non- perfect squares

Why do we need to be able to square and find the root of a number? Squares and square roots are used in the Pythagorean Theorem Squares and square roots are used frequently in Algebra

Remember how to calculate the area? 4 inches A = l w A = 4 in. 4 in. 4 inches A = 16 in. 2

A square must have the same length and width. 4 inches A = l w A = 4 in. 4 in. 4 inches

To square a number means to multiply it by itself. 5 squared means 5 x 5 Take the number 5 And square it!

There is a shorter way to write 5 x 5. Say: “5 squared” or “5 to the 2 nd power”.

These are the parts. This is the base This is the exponent

What are exponents? Remember multiplication is repeated addition: Exponents are repeated multiplication: 4 x 5 = = 4 x 4 x 4 x 4 x 4

What do the parts mean? Tells you what to multiply... Tells you how many... = 5 x5 x 5 x 5

Evaluate it! = 5 x5 x 5 x 5 B. 625A. 20

This is another formula for finding the area of a square. s A = s 2 s is the side length

Evaluate it! B. 49A. 14

Radicals (also called roots) are directly related to exponents.

The symbol used to indicate a root is the radical symbol -

Every radical expression has three parts… Index Radicand Radical

but is normally written as. The square root of 49 could be written as …

What does square root mean?

The square root of a number is another number which when multiplied by itself gives back the original number.

What is a square root? the measure of the side of the square 16 = 4 ?

What is the square root of 36? 36 =6

Example: because Also because

These numbers are called perfect squares

If a number is a perfect square, then you can find its exact square root. A perfect square is simply a number that can be written as the square of another number.

What are the first 10 whole numbers that are perfect squares? 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Not all numbers have an exact square root as in the previous examples.

What if you are asked to find the square root of a non-perfect square?

Find the two closest perfect squares. 16 = 4 The square root of 15 must be between 3 and 4, closer to 4. 9 = 3

20 would be between which two whole numbers? 25 = 5 16 = 4 20 Between 4 and 5

Use the next process to find a close approximation for the square root of 10.

Is 10 a perfect square? Can you make a square out of these ten tiles?

Is 10 a perfect square? Can you make a square out of these ten tiles?

Can we approximate (get close to) the square root of 10? You have to make a square out of the ten tiles

What is the length of each side? close ! Can we approximate (get close to) the square root of 10?

1 6 Is 3 a good approximation of 10 ? = 

Most standardized tests only ask for approximations like this: 153 is between which of the following consecutive whole numbers? A. 15 and 16 B. 9 and 10 C. 12 and 13 D. 76 and 77

1. A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly? 2. A metal bar weighs 8.15 ounces. 93% of the bar is silver. How many ounces of silver are in the bar? 3. Cost of sled: $99.50 Markup: 95% Find the selling price. 4. Cost of a comic book: $3.95 Markup: 20% Find the selling price.

Quiz 1. Evaluate Evaluate Evaluate is between what two consecutive whole numbers? and 15