Question

show how √5 can be represented on number line​

Answer 1

Step-by-step explanation:

Take a line segment AB = 2 units (consider 1 unit = 2 cm) on x-axis.

Draw a perpendicular on B and construct a line BC = 1 unit length.

Join AC which will be √5 (Pythagoras theorem). Take A as center, and AC as radius draw an which cuts the x-axis at point E.

The line segment AC represents √5 unit

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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=1unit.

We have OA=2 units and AB=1unit

Using pythagoras theorem, we have,

OB^2=OA^2+AB^2

OB^2=2^2+1^2

OB=

$\sqrt{5}$

Taking O as the centre and OB= root 5

as radius draw an arc cutting real line at C. Clearly, OC=OB=root 5

.

Hence, C represents root 5 on the number line