questions please

consider an integer 5. We can express 5 as the sum of squares of two numbers. So, we have 5 = 2² + 1² ⇒ (√5)2 = 2² + 1² The above equation follows the Pythagoras theorem with √5 as the hypotenuse, 2 and 1 as the other two sides of the right triangle respectively. This shows that we need to construct a right triangle with sides 2 units and 1 units so that the hypotenuse becomes √5 units on the number line. Observe the figure and the steps given below to represent root 5 on the number line. Let us see how to draw root 5 on number line.  Step 1: On the number line, take 2 units from 0 and represent this point as A. Therefore, segment AB = 2 units Step 2: At point B, draw a perpendicular and mark C such that BC = 1 unit. Join A to C. Using the Pythagoras theorem, we can see that AC is the hypotenuse because ABC is a right-angled triangle and the side opposite to the right angle is the hypotenuse. In △ABC, using Pythagoras theorem, we have AC² = AB² + BC² = 2² + 1² = 5 ∴ AC = √5 units Step 3: Now, with A as the center and AC as radius, draw an arc of radius AC to cut the number line at D. Since AC = AD, point D represents √5 on the number line. Since, AC = AD = √5 units, therefore, point D represents √5 on the number line. So, we learnt how to draw root 5 on number line. In this way, we can also locate root 5 on number line.

Show how root5 can be represented on the number line