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{5}

.

Accepted Answer

We are given to represent the number $2 + \sqrt{5}$ on the number line.

For this, first, we shall find the point representing $2$ on the number line. Then, we shall start from this point and obtain another point on the same number line in the same side of it, representing $\sqrt{5}$ . Combining these two points, we shall obtain the point representing $2 + \sqrt{5}$ .

Steps:

a) $O, A$ and $B$ represent numbers $0, 2$ and $4$ , respectively. So, $O A = 2$ units and $A B = O B - O A = 4 - 2 = 2$ units.

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

c) So, $A C = \sqrt{A B^{2} + B C^{2}} = \sqrt{2^{2} + 1^{2}} = \sqrt{4 + 1} = \sqrt{5}$ units. [By Pythagoras theorem]

d) Now, take a compass, take $A$ as centre and $A C$ as radius, draw an arc such that it intersects the number line at the point $P$ . So, $P$ is the point representing $\sqrt{5}$ on the number line and $2 + \sqrt{5}$ units.

e) Now, we see $O P = O A + A P = 2 + \sqrt{5}$ units.

Therefore, we have represented $2 + \sqrt{5}$ on the number line.

Locate on the number line, the point representing the number $2 + \sqrt{5}$ .

Important Questions on Number System

Learn and Prepare for any exam you want !

Locate on the number line, the point representing the number 2+5.

Important Questions on Number System

Learn and Prepare for any exam you want !

Locate on the number line, the point representing the number $2 + \sqrt{5}$ .