Question

Represent following irrational numbers on the number line:√2,√3,√5,√7,√11,√17​

Answer 1

Answer:

I will show how to represent root 11 and other do it yourself

Step-by-step explanation:

First draw a number line with center O.Take a point P with

distance OP=11 unit.

Take another point Q with distance OQ=1 unit.

So PQ=OP+OQ=11+1=12

Take a point M where M is the midpoint of PQ.

Therefore PM=MQ= ½PQ=6

Draw an arc with center M from point Q and draw a line perpendicular to PQ from point O which cuts the arc at point T.

As PQ and MT are radius of same arc, so MT=MQ=6

OM=OP-PM=11-6=5

Now ΔMOT is a right angled triangle with <MOT=90°

By using Pythagoras Theorem,

MT ² = OM² + OT²

Þ OT² = MT ² - OM²

Þ OT² = 6² - 5²

Þ OT = √11

Now drawing an arc with center O from point T to PQ,we get point R where the arc intersects the line PQ.

Since OT and OR both are radii of same arc,

So OT=OR=√11

Therefore √11 is placed at point R on number line.

Hope It Helps

Answer 2

Answer:

your answer

Step-by-step explanation:

have a great day