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Math 8R

Week 8

Distance Lessons Week 8 (5/18-5/22)

8R Distance Learning Week 8

M 5/18 11.1 A Rational and Irrational Numbers

CW Page 1 ONLY

HW #1 ONLY

A) Copy class notes into notebook (See Additional Notes below)

B) Answer homework question and check answers.

C) Check out the videos below for more information

Remember to Email us with any questions!

11.1 A CW

11.1 A HW

Additional Notes. This lesson describes all of the Real Sets of numbers. Check out the first 2 videos.

We are also deciding whether numbers are Rational (nice) or Irrational (not nice.)

As you can see in the picture to the right:

Rational are numbers that can be expressed as decimals that terminate (end) or repeat; Fractions that contain integers in the numerator and denominator; square roots of perfect squares. Any number that you can write as a decimal and walk away. 1/2 = 0.5 2/3 = 0.6
Irrational are numbers that can NOT be expressed as decimals that terminate (end) or repeat; Fractions that contain numbers like pi in the numerator and denominator; square roots of non-perfect squares. Any number that you canNOT write as a decimal and walk away. Notice the ... after some decimals.
DO NOT LOOK FOR PATTERNS! 1.23456789101112131415... is a number that contains a pattern yet it is NOT rational. It does NOT terminate or repeat.

11.1 A Suggested videos

Identifying Sets of Real Numbers

Real Numbers

First 3:15

Determine Rational or Irrational Numbers (Square Roots and Decimals Only)

T 5/19 11.1 B Square and Cube Roots

CW Page 2

HW #2, 3, 4

A) Copy class notes into notebook (See Additional Notes below)

B) Answer homework questions and check answers.

C) Check out the videos below for more information

Remember to Email us with any questions!

11.1 B CW

11.1 B HW

Additional Notes:

Square Root is the inverse of Squared. 3 squared is 9 because 3*3 = 9. The square root goes in the opposite direction. Square root of 9 is 3 because 3*3=9. When finding the square root, you want to know what times ITSELF gives that number.
Cube Root is the inverse of Cubed. 3^3 = 27 because 3*3*3=27. The cube root goes in the opposite direction. Cube root of 27 is 3 because 3*3*3=27. When finding the cube root, you want to know what times itself 3 times gives that number.

Check out the website for more information on Square and Cube Roots, then see the videos below.

11.1 B Suggested videos

Introduction to Square Roots

Simplify Square Roots (Perfect Squares)

Introduction to Square Roots With Area

W 5/20 Mixed Practice

Today you will continue practicing rules.

There are TWO Assignments!!

1. Complete the worksheet to the right (2 Pages.)

2. Log into Delta Math and complete assignment "8RDL Real and Pythag 1"

Remember to Email us with any questions!

ClassifyingRationalIrrationalNumbersPractice.doc

11.1 Additional Sheet Answers

Th 5/21 11.2 Simplifying Radicals

A) Copy class notes into notebook (See Additional Notes below)

B) Answer homework questions and check answers.

C) Check out the videos below for more information

Remember to Email us with any questions!

11.2 CW

11.2 HW

*Ignore the yellow highlighting

Additional Notes.

In order to simplify radicals, you need to know your perfect squares. Either list them first or have them in front of you for reference. Let's do a few from the Classwork.

1. rad18 Break 18 into the product of 2 numbers where 1 is a perfect square (but you cannot use 1). 18 is 18*1, 9*2, and 6*3. The only pair with a perfect square is 9*2 so we must use them. ALWAYS write the prefect square in front of the non-perfect square. When you take the square root it will become the coefficient in the front. So rad18 = rad9*rad2 We know rad9 = 3 so the answer is 3rad2.

2. Number 1 rad12. Break 12 into the product of 2 numbers where 1 is a perfect square (but you cannot use 1). 12 is 12*1, 6*2, and 4*3. The only pair with a perfect square is 4*3 so we must use them. ALWAYS write the prefect square in front of the non-perfect square. When you take the square root it will become the coefficient in the front. So rad12 = rad4*rad3 We know rad4 = 2 so the answer is 2rad3.

3. Number 9 rad75. Break 75 into the product of 2 numbers where 1 is a perfect square (but you cannot use 1). 75 is 75*1, 25*3, and 15*5. The only pair with a perfect square is 25*3 so we must use them. ALWAYS write the prefect square in front of the non-perfect square. When you take the square root it will become the coefficient in the front. So rad75 = rad25*rad3 We know rad25 = 5 so the answer is 5rad3.

If you choose the LARGEST perfect square, you only have to do the work once.
If you choose a SMALLER perfect square, you will have to do the problem multiple times until it is simplified COMPLETELY.

Let's take a look at number 6 -rad72. First I want to mention the negative. Just bring that down to the answer. Now lets look at the factors - 1*72, 2*36, 3*24, 4*18, 6*12, and 8*9. There are 3 perfect squares in there. If we use the LARGEST, which is 36, it will be the easiest. If we use 4 or 9, we are going to have to simplify twice. All 3 methods are shown below.

ALWAYS USE THE LARGEST PREFECT SQUARE WHEN SIMPLIFYING!

11.3 additional

11.2 Suggested videos

Simplifying Radicals

First 8 minutes

How To Simplify Radicals

First 3:42

How to Simplify Radicals (NancyPi)

F 5/22 Simplifying Radicals Practice

Today you will continue practicing rules.

Log into Delta Math and complete assignment "8RDL Real and Pythag 2"

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