Show how root 5 can be represented on the number line

Question – Show how root 5 can be represented on the number line

Solution:

Follow the steps below to represent √5 on the number line as show in the figure above:

Step (I) : Consider a right angled triangle OAB on the number line as shown in figure with
OA = 2 units
AB = 1 unit.
Then by using Pythagoras theorem we can easily find

(Hypotenuse)² = (Base)² + (Perpendicular)²

OB² = OA² + AB²

OB = √(2² + 1²) = √5

Step (II) : Using a compass , draw an arc with centre O and radius OB intersecting the number line at C. Then C corresponds to √5 on the number line.

Related Questions –

• State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form √m , where m is a natural number. (iii) Every real number is an irrational number.
• Are the square root of all positive integers irrational If not give an example of the square root of a number that is a rational number