 Hi and how are you all today? Let us do a very interesting question today. It says show how root 5 can be represented on the number line. Now to show how to find root 5 for any given positive real number geometrically we will be using geometrical method for it. For this mark a distance of 5 units from a fixed point A. Let us name this point as A and mark a distance mark a point B at a distance of 5 units from point A such that AB is equal to 5 units. Now from B mark a distance of 1 unit of 1 unit and mark the new point as C. Now find the midpoint of AC and mark a point O on it. Draw a semicircle with centre O and radius equal to OC. So draw a line perpendicular to OC passing through point B and intersecting the semicircle at point D. So perpendicular means the angle BC or CBD should be equal to 90 degrees. Right? And then BD is equal to root 5. Right? So in this way we can represent root 5 on a number line. Let me write down the steps of constructions for you so that by any point you will not forget how you did it. First of all mark the distance of 5 units since we need to represent root 5. So we will mark a distance of 5 units from a fixed point where AC is representing our number line. Right? So 5 units means you can take any unit to this, obtain a point B such that AB is equal to 5 units. Right? Second step you did was from B mark a distance of 1 unit and mark the new point. Right? Third step it will be find the midpoint of AC and name it as O. Then what you did exactly? Taking OC as the radius, draw a semi-right. Then fifth point says draw a line perpendicular to AC passing through and intersecting the semicircle BD is equal to root 5. Right? So this entire process completes the question that was given to us. Try to make your figure as neatly as possible. Bye for now.