Starting from point on a number line

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

Problem

Starting from point

0

on a number line, a student constructs successively the distances

\sqrt{2},\sqrt{3},\sqrt{4},\ldots

so that each new distance is obtained from the previous one in a single additional step. (i) Carry out this process to obtain points representing

\sqrt{13}

and

\sqrt{17}

. Write each step of the construction in order. (ii) Prove algebraically that the lengths obtained in part (i) are

\sqrt{13}

and

\sqrt{17}

respectively. (iii) Using your diagram, indicate the relative positions of

\sqrt{10}

\sqrt{13}

and

\sqrt{17}

on the number line and justify the order shown.