Question

Classify the following numbers as rational or irrational : 

(i) √23

(ii) √225

(iii) 0.3796 

(iv) 7.478478 

(v) 1.101001000100001…

Answer 1

(i) √23 = 4.7958………. 

This is not terminating or non-recurring decimal. 

∴ √23 is an irrational number. 

(ii) √23 = 15 this is a rational number. 

(iii) 0.3796 

This is rational number, because trminating decimal has expansion. 

(iv) 0.478478… 

This is rational number, because decimal expansion is recurring.

 (v) 0.101001000100001… 

This is an irrational number because termianting or recruring decimal has no expansion.