We have seen in class 7 that any odd number can be written as the difference of two perfect squares. (The lesson identities) Using this, drawn lines of length `sqrt7` and `sqrt11` centimetres.

We have seen In Class 8 that any odd number can be written as the difference of two perfect squares. Using this, draw squares of areas 7 and 11 square cențimetres.

Explain two different method of drawing a line of lengths sqrt13 centimetres.

How many distinct 3 digit numbers can be written using the digits 5,6 and 7 without repeating the digits? a) What is the probability that the numbers are odd numbers? b) What is the probability that the numbers are even numbers?

We have seen that the points (3,5),(6,7),(9,9) are points on the same line. is there any relation between the 'x' coordinates 3,6 .and 9 of these points? What about the y coordinates 5,7,9 ? Can you find some more points on this line with natural number coordinates?

We know that sequence got by starting with any number and adding a fixed number repeatedly is called an arithmetic sequence.Example: 1,3,5,7,........ Like this we can form sequences by starting with any number and multiplying by a fixed non-zero number repeatedly. For example 1,2,4,8.......... In this sequence, one number multiplied by 2 gives the next number. Such sequences are called geometric sequences. The common number used for repeated multiplication is called common ratio. What is the common ratio of the geometric sequence 3,12,48,.....?