# Textbook

1. Karnataka text book for Class 10, Chapter 07 - Surds

1. 9th_and_10th_ NCERT, ICSE and CBSE Text books, relavent websites and other books

## Useful websites

1. Surds starts with basic concepts,(to view the next page, please click on previous/up/next options in the bottom of the page
3. surds and other rootsThis page discusses surds and roots in detail.
4. Video on Surds from Youtube :simplifying surds,rationalising surds,dividing and multiplying surds

## Reference Questions

1. what is the meaning of surds?
2. Difference between like and unlike surds.
3. Meaning of Pure and mixed surds.
4. Simplification of rationalising the denominator.

# Teaching Outlines

• Definition, examaples
• Order and radicand of a surd
• Like Surds and Unlike Surds
• Addition and Subtraction of Surds
• Multiplication of Surds.
i.Multiplication of Surds having same Order
ii. Multiplication of Surds having different Order
• Rationalising Factor of a Surd
• Simplifying a surd by Rationalizing denominator of a surd

## Concept 1: Definition of surds

Irrational root of rational number. Example:${\displaystyle {\sqrt {2}},7{\sqrt {5}},{\sqrt {x}}}$

### Learning objectives

1. know the meaning of surds
2. recognising radicand and order of surds

### Notes for teachers

If you can't simplify a number to remove a square root (or cube root etc) then it is a surd. If it is a root and irrational, it is a surd. But not all roots are surds.

### Activities

Activity for Definition click

## Concept-2: Like and Unlike surds

### Learning objectives

1. Know the meaning of surd
2. recognising the meaning of order and radicand
3. Examples of like and unlike surds
4. To change surd to simplest form
5. Addition and Multiplication og surds

### Notes for teachers

1.Like surds: A group of surds having same order and same radicand in their simplest form. Example: ${\displaystyle 3{\sqrt {5}},7{\sqrt {5}},x{\sqrt {5}}}$
2.Unlike surds: Groups of surds having different orders or different radicandsor both in their simplest form. Example: ${\displaystyle {\sqrt {a}},3{\sqrt {2}},x{\sqrt {5}}}$
3.Addition and sustraction of surds. Example: ${\displaystyle 2{\sqrt {5}}+3{\sqrt {5}}-{\sqrt {5}}}$
4.Multiplication of surds. Example: ${\displaystyle 7{\sqrt {3}}X2{\sqrt {5}}}$

### Activities

1. simplify the surds

${\displaystyle 3{\sqrt {45}}+2{\sqrt {20}}-{\sqrt {5}}}$

${\displaystyle =3{\sqrt {3X3X5}}+2{\sqrt {2X2X5}}-{\sqrt {5}}}$

# Assessment activities for CCE

Solving problems with same order and same radicand, same order and different radicand, different order and different radicand also different order and same order. Examples: Surds_CCE_Activity click here