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square root

Suppose N is a natural number such that N=$m^{2}$ . The number m is called square root of N we have $m^{2}$=mxm or $(m)^{2}$=-mx-m. Thus $m^{2}$ has 2 square roots, m and -m. Example 9=$3^{2}$ or $(-3)^{2}$.Thus both 3 and -3 are ${\sqrt {9}}$

Textbook

8 and 9 maths text books of Karnataka state
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Additional information

Useful websites

you can play with perfect square numbers from 1 to 1000 & play games with numbers please click here

To estimate the square root of a number click here

To play quiz on square root of a number click here

Reference Books

This text book contains activities for students to understand square and square root NCERT 8th std maths text book of chapter 6

Teaching Outlines

Concept #1

'perfect square-numbers'

Learning objectives

1. The students should understand that a perfect square number is the product obtained by multiplying same number with same sign twice.
   
2. Recognising perfect square-numbers in a given group of numbers
   
3. perfect square-number patterns
   
4. differentiating between perfect square-numbers & other numbers.
   

Notes for teachers

Patterns & games of perfect square-number may be given to students

Activity No 1

On a paper make 3 columns like N , NxN & product .give some numbers under column N and students can fill the other 2 columns

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• Materials/ Resources needed :- One white paper with 3 columns likeN , NxN &product.Pen or pencil to every student
• Prerequisites/Instructions, STUDENTS SHOULD PERFECTLY KNOW ABOUT MULTIPLICATION OF NUMBERS
• Multimedia resources INTERNET ,
• Website interactives/ links/ simulations Inthis web site you can play with perfect square number s from 1 to 1000 & play games with numbers.
• Process/ Developmental Questions
  1) the side of a square is 15 cm .what is area of square ?
  2) 121 balls are arranged in square pattern .How many balls in each row?
• Evaluation
  1) squqre of 15 =........
  2)144 =........... writte in the form n2
• Question Corner

Activity No 2

Click to Comment

• Materials/ Resources needed :-
• Prerequisites/Instructions,
• Multimedia resources
• Website interactives/ links/ simulations
• Process/ Developmental Questions
  
• Evaluation
  
• Question Corner

Activity No 3

Click to Comment

• Materials/ Resources needed :-
• Prerequisites/Instructions,
• Multimedia resources
• Website interactives/ links/ simulations
• Process/ Developmental Questions
  
• Evaluation
  
• Question Corner

Concept #2

SQUARE ROOT OF A NUMBER

Learning objectives

1. Understanding the geometric meaning of square root.
2. Finding square root of a perfect square number by prime factorisation.>
3. Finding square root of a number by division method.
4. Finding square root of a decimal number.

Activity No 1 Activity on square and square roots by exploring the relationship between area of a square and its side length

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• Estimated Time :

40 minutes.

• Materials/ Resources needed :Laptop, geogebra file, projector and a pointer.
• Prerequisites/Instructions:

1. The students should know tables and multiplication .
2. They should know that the product obtained by multiplying the same number twice is called a perfect square number and the number itself is called its square root.
3. They should know a square , its side length and finding area of a square.

• Multimedia resources : Laptop
• Website interactives/ links/ simulations
• Process:

1. Initially the teacher can discuss about a square, its sides and area of a square.
2. Tell the students that each small inner square measures 1 unit .
3. Formula to find area of square is side X side.
4. Each inner square's area is 1 sq unit.
5. Start with a outer big square of side length 3, which gives an area of 9. Then after doing side lengths of 3-5, put up a square and say the area is 64, so what must the side lengths be? The students will know it must be 8. Do this a few times and then introduce the new notation saying that the side length for the square with area 64 is the sqrt(64) = 8, and that is along the side of the square. Similarly repeat for area 144 and write it as square root of 144 =12 on the side length. Tell them that a square root is the inverse of squaring a number.
6. Introduce the symbols forsquare and square root.

Extending the analogy to the area of a square and its side length helps students visualize the geometric meanings of square and square roots. [Note : Disadvantage of this activity: here we can consider only positive numbers as square roots. Hence in further classes the concept of square root should be extended to negative numbers as well.]

• Developmental Questions:

1. What is the figure called ?
2. How do you know its a square ?
3. Why is the figure called a perfect square ?
4. What are the dimensions of each inner smaller square ?
5. What is the area of each small inner square ?
6. What is the area of two such small squares ?
7. What is the area of 9 such small squares ?
8. If the small squares are of 1 unit dimension, and area of each such square is one sqcm, can we say that the whole area is equal to the total number of smaller squares.
9. (The number of cells/small squares in each row) x (number of rows) gives us ________.
10. If the number of cells in each row and number of rows is same then we multiply the _________ number twice.
11. Conversely if area is known, then its ___________ can be found out.
12. For ex : If the area of a square is 81, then what would be its side length?

• Evaluation :

1. Did students make the connection between the area of a square and square numbers? How do you know?
2. What evidence helped you assess students' understanding of the geometric meaning of square root?

• Question Corner:

1. If you know the side length of a square, how can you determine its area?
2. If you know the area of a square, how can you determine its side length?

Activity No 2

Click to Comment

• Materials/ Resources needed :-
• Prerequisites/Instructions,
• Multimedia resources
• Website interactives/ links/ simulations
• Process/ Developmental Questions
  
• Evaluation
  
• Question Corner