Question

$\sqrt{5 } \: on \: real \: number \: line \:$
​

Answer 1

Draw number line as shown in the figure. Let the point O represent 0(zero) and point A represents 2. Draw perpendicular AX at A on the number line and cut-off arc AB = 1 unit.

We have OA = 2 unit and AB = 1 unit

Using pythagoras theorem, we have,

OB² = OA² + AB²

OB² = ( 2 )² + 1² = 5

$\sf \: OB = \sqrt{5}$

$\sf \: Taking \: O \: as \: the \: centre \: and \: OB = \sqrt{5}$

as the radius draw an arc cutting real line at C. Clearly,

$\sf \: OC = OB = \sqrt{5}$

$\sf \: Hence, C \: represents { \mathfrak \red{\sqrt{5}}} \: on \: the \: number$

number line.

Answer 2

Answer:

Draw number line as shown in the figure. Let the point O represent 0(zero) and point A represents 2. Draw perpendicular AX at A on the number line and cut-off arc AB = 1 unit.

We have OA = 2 unit and AB = 1 unit

Using pythagoras theorem, we have,

OB² = OA² + AB²

OB² = ( 2 )² + 1² = 5

\sf \: OB = \sqrt{5}OB=

5

\sf \: Taking \: O \: as \: the \: centre \: and \: OB = \sqrt{5}TakingOasthecentreandOB=

5

as the radius draw an arc cutting real line at C. Clearly,

\sf \: OC = OB = \sqrt{5}OC=OB=

5

\sf \: Hence, C \: represents { \mathfrak \red{\sqrt{5}}} \: on \: the \: numberHence,Crepresents

5

onthenumber

number line.