Template:Subst;square roots

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Concept Map
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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 $$\sqrt9$$

= Textbook = 8 and 9 maths text books of Karnataka state To add textbook links, please follow these instructions to: ([ Click to create the subpage])

= 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
 * 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

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

Activity No 3

 * 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
40 minutes. 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.]
 * Estimated Time :
 * 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.
 * 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

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

= Project Ideas =

= Fun corner =