Question

Locate $\sqrt{3}$ on the number line.

Answer 1

Hint: We will take 1 unit on x axis and 1 unit on y axis and with that we get the hypotenuse as $\sqrt{2}$ and then with compass we will cut the axis to plot it, again we will take base as $\sqrt{2}$ and then we will get the hypotenuse as $\sqrt{3}$ which will be then again using compass we will plot $\sqrt{3}$.

Complete step by step answer:

First we have taken a right angle triangle ACD , the hypotenuse of this triangle is $\sqrt{2}$ ,
Then we draw a curve of radius $\sqrt{2}$ from C which cuts the x axis at point E which is the value of $\sqrt{2}$ on the number line.
Similarly we have taken right angle triangle EFC with base $\sqrt{2}$ and height 1, we get hypotenuse $\sqrt{3}$
Now again drawing an arc it cuts the x axis at G.
The point G that we have marked is the value of $\sqrt{3}$ and hence we have shown the value of $\sqrt{3}$ in the number line.
Hence $\sqrt{3}$ has been located on the number line.

Note: We know that $\sqrt{3}$ is irrational number and hence to plot the exact value of $\sqrt{3}$ is very much difficult so we have taken an approximate value of $\sqrt{3}$ and then we have plotted the approximate value in the number line. One important point one should keep in mind is that we can find one irrational number between any two rational numbers and one can also find one rational number between any two irrational numbers.