Real numbers

While creating a resource page, please click here for a resource creation checklist.

= Concept Map =

= Textbook = To add textbook links, please follow these instructions to: ([ Click to create the subpage])

=Additional Information=

Reference Books
{7} over {6}

= Teaching Outlines =

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

= Hints for difficult problems = Irrational numbers Exercise 1.3.1

1.Write four possible irrational numbers between 4 and 5.

Solution:

Consider the squares of 4 and 5

Square of 4 = 16 and Square of 5 = 25

We can also write 4 and 5 as √ 16 =4 and √ 25 =5

Between  and there exists

√ 17 ,√ 18, √ 19 , √ 20 , √ 21 , √ 22 , √ 23 , √ 24

Use the following Geogebra applet to Visualise Rational and Irrational Numbers

<ggb_applet width="800" height="400" version="4.4" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />

= Project Ideas =

= Math Fun =

Usage

Create a new page and type to use this template