We have seen how to obtain a line whose length is a rational number.
How do we obtain lines whose lengths are irrational? [Page No. 55]

Using the Baudhāyana–Pythagoras theorem, instead of trying to measure a fraction.

Build a right-angled triangle whose two legs have nice rational lengths; the hypotenuse can then come out irrational. For $\sqrt{2}$, make both legs 1 unit: the hypotenuse is $\sqrt{(1^2 + 1^2)} = \sqrt{2}$.

A ruler cannot mark $\sqrt{2}$ as a fraction of a unit, but a right angle constructs it exactly. A compass can then swing that length down onto the number line to mark the point $\sqrt{2}$.