Question

Represents the irrational numbers on the number line.

Answer 1

Represents the irrational numbers on the number line:

A number line is a pictorial representation of numbers on a straight line. It’s a reference for comparing and ordering numbers. It can be used to represent any real number that includes every whole number and natural number.

Irrational number

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0.

Examples: $\sqrt{2},\sqrt{5},\sqrt{11},\pi \left(Pi\right)$

Representation of $\sqrt{\mathbf{5}}$ on the number line

As illustrated in the image, draw a number line. Let $0$be represented by a point $O$ and $2$ by point $A$. On the number line, draw perpendicular $AXatA$ and cut-off arc $AB=1$ unit.
We have $2$ units of $OA$ and $1$ unit of $AB$.

• $OA=2$ units
• $AB=1$unit

By pythagoras theorem

$O{B}^2=O{A}^2+A{B}^2$

$\Rightarrow$ $O{B}^2=2^2+1^2$

$\Rightarrow$ $O{B}^2=4+1$

$\Rightarrow$$O{B}^2=5$

$\Rightarrow$$OB=\sqrt{5}$

Taking $O$ as the centre and $OB=\sqrt{5}$as radius draw an arc cutting real line at $C$. Clearly, $OC=OB=\sqrt{5}$.

Hence, $\mathit{O}\mathit{C}$ represents$\sqrt{5}$on the number line.