Question

show how √5can be represent on the number line​

Answer 1

$\large\red{\boxed{\purple{STEPS\:OF\:CONSTRUCTION}}}$

★First draw a number line & mark equal divisions.

★Number the divisions as 0,1,2,3...as per requirement.

★At 0 mark point 'O'.

★Taking O as centre construct 90° on it.

★Extend the perpendicular line as per requirement.

★Now, taking O as center cut an arc of unit length. Mark it. say A

★Taking two divisions join it with point cuted on the perpendicular.

Now, ∆ OAB is a right angled triangle at O.

★Taking AB as radius & O as center cut an arc on the number line.

★Hence this arc at number line from O represents √5.

_________________________________

Proof of AB = √5.

In ∆OAB,

$\large\green{\boxed{\orange{AB^{2}=OB^{2}+OA^{2}}}}$

(By Pythagoras Theorem)

$\implies AB^{2}=2u^{2}+1u^{2}$

$\implies AB = \sqrt{4+1}$

${\underline{\boxed{\red{.\degree. AB =\sqrt{5}}}}}$

$<marquee scrollamount="1300">♥Answer by Rishabh♥</marquee>$