Question

show how
$\sqrt{m}$
can be rapresented on the number line? ​

Answer 1

Case 1:

$m$ is a perfect square.

So, let $m=k^2$

Therefore,

$\sqrt{m} = k$

Hence, $k$ can be easily represented on the number line, as it is a real number.

Case 2:

$m$ is not a perfect square.

Now, we need to split $m$ into sum of two squares, by using the concept of Pythagorus Theorem.

$\sqrt{m}^2 = k_{1} ^{2} + k_{2} ^{2}$

Now, draw $k_{1}$ on number line as the Base, and draw $k_{2}$ as the Perpendicular.

At last, the Hypotenuse would be $\sqrt{m}$, So we open our compass with radius $\sqrt{m}$, and cut an arc on the number line.

Hence, $\sqrt{m}$ has been represented on the number line.