Question

Show the number √5 on the number line.

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Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

To represent √5 on the number line, let's consider 5.

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.

On the number line, take the number 2 as point A, O as origin. With OA as base construct perpendicular at A and mark on it a point B such that AB is of unit length.

Join OB. ∴ OB = √5 units

With O as center and radius equal to OB, draw an arc that cuts the real line at X. Then OX is of √5 units.

X represents the number √5 on the real line.