Question

represent the real number root 2 root 3 root 5 on a single number line​

Answer 1

this is the answer and I hope it will help you .

Answer 2

Answer:

The required number line for $\sqrt{2} \sqrt{3} and\sqrt{5}$

Step-by-step explanation:

Explanation:

Draw a number line .

Taking OA  = 1 unit

Draw AB perpendicular  on OA

such that AB = 1 units  and let OA = 1 unit

Step1:

Now from pythagoras theorem

$OB = \sqrt{(OA)^{2} +(AB)^{2} }$

   = $\sqrt{1^{2} +1^{2} }$

   = $\sqrt{2}$

Now taking length of OB and  from the centre draw an arc through compass which cut the number line .

So , the intersect point on the number line  is $\sqrt{2}$

For $\sqrt{3}$ :

Draw  CB perpendicular on OB

Such that OB = $\sqrt{2}$ unit  and let CB = 1 unit .

Therefore by pythagoras theorem

$OC = \sqrt{1^{2} +\sqrt{2} ^{2} }$

      = $\sqrt{3}$

Now taking length of OC and draw an arc through compass which cut the number line .

So , the intersect point on the number line  is $\sqrt{3}$

Similarly for $\sqrt{5}$ :

Draw DC perpendicular on OC

such that OC = $\sqrt{3}$ unit  and let DC = $\sqrt{2}$.

By pythagoras theorem

$OD = \sqrt{\sqrt{2} ^{2} +\sqrt{3} ^{2} }$

    = $\sqrt{5}$.

Now taking length of OD and draw an arc through compass which cut the number line .

So , the intersect point on the number line  is $\sqrt{5}$.

Final answer:

Hence , here we represent the real number $\sqrt{2} \sqrt{3} and \sqrt{5}$ on the number line .