Show how √5 can be represented on the number line.
Solution:
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 and 1 units so that the hypotenuse becomes √5 units on the number line.
We shall proceed as follows.
Step 1: On the number line, take 2 units from O and represent the point as A.
Step 2: At point A, draw a perpendicular and mark B such that AB = 1 unit.
Step 3: Now, with O as the center and OB as radius, draw an arc to cut the number line at C.
Step 4: Point C represents √5 on the number line.
In △OAB, using Pythagoras theorem, we have
OB² = OA² + AB²
= 2² + 1²
= 5
∴ OB = √5 units
Since, OB = OC = √5 units, therefore, point C represents √5 on the 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 C 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.