A student wrote down the four numbers ,

MATHEMATICS · Subjective · CBSE · Mathematics · Number Systems · Number Systems

Problem

A student wrote down the four numbers

0.375

0.070070007\ldots

\sqrt{49}

and

\sqrt{50}

. (i) Explain clearly why

0.375

is a rational number. (ii) The decimal

0.070070007\ldots

is formed by inserting one more zero between successive 7’s. Explain why this number is irrational. (iii) Compare the nature of

\sqrt{49}

and

\sqrt{50}

and justify, with reasons, whether each is rational or irrational.