Show how √5 can be represented on the number line.
Solution: Let us see how to represent root 5 on number line.
It requires a little accuracy to show root 5 on number line.
To represent √5 on the number line, let's 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.
☛ Check: Class 9 Maths Chapter 1 NCERT Solutions
Video Solution:
Show how √5 can be represented on the number line.
NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.2 Question 3
Summary:
√5 can be shown on the number line by constructing a right triangle of appropriate measures followed by the application of Pythagoras theorem. Point D on the number line represents √5.
☛ 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 roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.