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.

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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.