Question

represent root 2, root 3, root 5, root 6. on number line

Answer 1

Answer:

where is root 6 in the answer

Step-by-step explanation:

anybody please show me how to locate root 6 on the numberline please

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 $A B=1$ units and let $O A=1$ unit

Step1:

Now from Pythagoras's theorem

$\begin{aligned}&O B=\sqrt{(O A)^{2}+(A B)^{2}} \\&=\sqrt{1^{2}+1^{2}} \\&=\sqrt{2}\end{aligned}$

Now take the length of $OB$ and from the center draw an arc through a compass which cut the number line.

So, the intersecting 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

$\begin{aligned}O C &=\sqrt{1^{2}+\sqrt{2}^{2}} \\&=\sqrt{3}\end{aligned}$

Now taking length of$\mathrm{OC}$ 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

$\begin{aligned}O D &=\sqrt{\sqrt{2}^{2}+\sqrt{3}^{2}} \\&=\sqrt{5}\end{aligned}$

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 $\sqrt{5}$.

Hence, here we represent the real number $\sqrt{2} ,\sqrt{3}$ a n d $\sqrt{5}$ on the number line