Name: Surds: Introduction
Uploaded: 2019-07-19
Duration: 4 min 21 s
Description: We know that irrational numbers are written in the form of neither terminating nor recurring decimals. Let's learn to write another form of irrational number...

Question

Locate on the number line, the point representing the number

2 \sqrt{3}

.

Accepted Answer

We are given to represent the number $2 \sqrt{3}$ on the number line.

For this, first, we shall find the point representing $\sqrt{3}$ on the number line and then, find another point on the number line which is at twice the distance of $\sqrt{3}$ .

Steps:

a) $A$ and $B$ represent numbers $0$ and $1$ , respectively

b) Draw $B C ⊥ A B$ , such that $B C = 1$ unit.

c) So, $A C = \sqrt{A B^{2} + B C^{2}} = \sqrt{1^{2} + 1^{2}} = \sqrt{1 + 1} = \sqrt{2}$ units. [By Pythagoras theorem]

d) Draw $C D ⊥ A C$ , such that $C D = 1$ unit.

e) So, again, by Pythagoras theorem, we get, $A D = \sqrt{A C^{2} + C D^{2}} = \sqrt{{(\sqrt{2})}^{2} + 1^{2}} = \sqrt{2 + 1} = \sqrt{3}$ units.

f) Now, take a compass, take $A$ as centre and $A D$ as radius, draw an arc such that it intersects the number line at the point $P$ . So, $P$ is the point representing $\sqrt{3}$ on the number line and $A P = \sqrt{3}$ units.

f) Again, take $P$ as centre and $A P$ as radius, draw another arc on the same side of the number line such that it intersects it at the point $Q$ . So, $Q$ represents the point $2 \sqrt{3}$ on the number line and $A Q = 2 \sqrt{3}$ units.

Therefore, we have represented $2 \sqrt{3}$ on the number line.

Locate on the number line, the point representing the number $2 \sqrt{3}$ .

Important Questions on Number System

Learn and Prepare for any exam you want !

Locate on the number line, the point representing the number 23.

Important Questions on Number System

Learn and Prepare for any exam you want !

Locate on the number line, the point representing the number $2 \sqrt{3}$ .