 Hello and welcome to the session. In this session we will learn about irrational numbers. Now we know that the rational numbers are the numbers in the form 2 over q where p and q are integers are not equal to 0. The irrational numbers cannot be expressed over q over integers p and q. So we can say a number which is not rational to rational number. Also rational numbers are represented by non-terminating, non-repeating decimals. Now the square roots root 3, root 5 and so on root 2 is equal to 1.41, 4 2, 1 3, 5 6 and so on and root 3 is equal to 1.73, 2 0, 5 0 8 and so on. That means these are non-terminating which means they are never ending and non-repeating decimals. Also the ratio of the circumference of any circle to its diameter is the irrational number. That means which is equal to 3.14159 rational number as this decimal is also non-terminating and non-repeating. Now let us discuss how to draw root 2 on the number line. Now for drawing root 2 on the number line in the first step draw which is denoted by L. So here we have drawn a number line which is denoted by L. Now in the second step and B on the number line 0 and B is at 1 so that A B is equal to 1 unit. So we have taken this point as A, this point as B such that A B is equal to 1 unit. Now in the next step draw a perpendicular line L point B such that B C is equal to 1 unit. So we have drawn a line M which is perpendicular to this line L at the point B and B C is equal to 1 unit. Now in the next step join, we have joined with A as center, name that point of intersection center and A C as the radius we have drawn a circular arc the point D. Now here we have written a triangle ABC which is right-handed at B and B C is equal to 1 unit and A B is also 1 unit. So in triangle ABC is equal to AB square which is base square plus square which is BC square. So this implies AC square is equal to AB square which is 1 square plus BC square which is also 1 square and is equal to 1 plus 1 which further gives AC is equal to root 2 units. Now you can see now we have that therefore AC is equal to AD is equal to root 2 unit of the same circle. Equal to root 2 units you can see that the point D that is this point. So this is how we can draw root 2 on the number line. Now let us draw root 5 on the number line. We have drawn a number line now in the second step Q is equal to 2 units. So we have taken this point SP and this point is Q such that PQ is equal to 2 units. Now in the next step draw a perpendicular Q such that equal to 1 unit at the point Q such that QR is equal to 1 unit. We have joined so with period center and radius we have drawn a circular arc which intersects the line A to the point D. There is a right angle triangle with PQ as 2 units QR as 1 unit. So in triangle by Pythagoras theorem is equal to base square perpendicular square which is QR square. Now PD are the radial equal to PD these are radial PD is equal to root 5 units. Now PD the point D that is this point corresponds to the V of Pythagoras. Let us start with the steps of construction. In the first step draw a root 2 line constructing with base perpendicular Pythagoras' sketch is equal to the right angle at B in which the base AB is 1 unit, the perpendicular BC is 1 unit and the high-flying AC is root 2 units. Now in the second step of perpendicular of length 1 unit another triangle 1 unit square which is CD square. AD square is equal to AC square which is root 2 square 1 square which is equal to 2 plus 1 is equal to root 3. Now in AD a wheel is constructed and this is the wheel we have constructed the triangle ABC. Then in the next step we have constructed the triangle ACD. Then after this we will construct the triangle AGE with AD as the base DE which is 1 unit and we are getting AE is equal to root 4 on the same way we will get learnt about irrational numbers. Then drawing the irrational numbers on the number line hope you all have enjoyed the session.