Subject – Mathematics Class – VIII Duration – 35 minute

 A child will able to correlate squares with previous knowledge.  A child will able to identify the square numbers.  A child will able to recall the properties of square numbers.  A child will able to find out the numbers between square numbers.

 Audio-Visual method.  Discussion method.  Inductive Approach of Learning.  Analytical Approach.  By Activity

We know about the area of square = side side. If side of square is 2cm, what will be its area? Given, side = 2cm Area of square = side side = 2 2 = 4cm² The numbers that can be expressed as the product of the number with itself. Such as 1,4,9,16,25….. are known as square numbers.

Number  1  2  3  4  5  11  12  13  14  15  16  1  4  9  16  25  121  144  169  225  256 Squares

1. If we square an even number we get an even number. for example: 2² = 4 6² = If we square an odd number we get an odd number. for example: 3²= 9 7² = Its not compulsory when a number ends with 0,1,4,5,6or 9 at its units place then it is always be a square number. For example :- Is 1069 a perfect square? No, 1069 is not a perfect square. When we multiply = 1089.

 Consecutive no. is a list of interval which occur at fixed interval. It may be in ascending order and descending order.  Consider a number 7² consecutive no's can be found as  1 st number = n²-1/2 2 nd number = n²+1/2 first number = 7²-1/2 = 24 second number = 7²+1/2 = 25 Q1. Express the following as the sum of the two consecutive numbers? A) 21² B) 19²

 We consider a number = 143 = 12²-1 It can be come from (a+1) (a-1) = a²-1 Q1. Find the product of two consecutive numbers between 44 and 46?

 Consider a number 39, we have to find the square of 39 without multiplication 39²=(30+9)²=30²+30x9+9x30+9² (a+b)² = a² + ab +ba + b² = =1521 Question no.1 Find the square of 42 without actual multiplication?

Q1. Find out the perfect squares?

Here we are discussing about positive square root of natural number. Positive square roots of a number is denoted by the symbol √. Example: - Square root of 64 2│64 2│32 2│16 2*2*2*2*2*2 = 2*2*2 2│8 = 8 2│4 2│2 │1 Q1. Find the square root of the 7056?

Example 1:- Square root of Square root of 729 = Q1. Find the square root of 1296.

 If a natural number m can be expressed as n², where n is a natural number, then m is a square number.  All square numbers end with o,1,4,5,6 or 9at unit’s place.  Square numbers can only have even number of zeroes at the end.  Square root is the inverse operation of square.  Positive square root of a number is denoted by the symbol of √.

 Today, we have studied about the square numbers and properties of it.  After that we have discussed the sum of consecutive number by using (n²-1/2) and (n²+1/2).  We have discussed about the product of consecutive number by using a²-1  We have also discussed how to find square of a no. by without multiplication.  We have discussed how to find square roots of a no. and its symbol.  We have also discussed one method of finding square roots by division method.

Find out the numbers whose square is this? Or Find out the square root of these numbers?

Q1. What will be the unit digit of the squares of the following numbers? a b c. 272 Q2. The squares of which of the following would be odd numbers? a b. 431 c Q3. Find the square of the following without multiplication? a. 93 b. 86