On the same number line

MATHEMATICS · Multi-part · CBSE · Mathematics · The Baudhayana-Pythagoras Theorem · The Baudhayana-Pythagoras Theorem

Problem

On the same number line, obtain the positions of

\sqrt{13}

and

\sqrt{\dfrac{13}{2}}

. (i) Carry out a suitable construction to locate

\sqrt{13}

and mark it as point A. (ii) Without starting a fresh construction, use point A to obtain the point B representing

\sqrt{\dfrac{13}{2}}

on the same number line. (iii) Give a mathematical justification showing that the length OB (where O is the origin) is indeed

\sqrt{\dfrac{13}{2}}

units.