Classify The Following Numbers As Rational Or Irrational : (i) root of 23 (ii)root of 225 (iii)0.3796 (iv)7.478478... (v)1.101001000100001…

Classify The Following Numbers As Rational Or Irrational : (i) root of 23 (ii)root of 225 (iii)0.3796 (iv)7.478478.. (v)1.101001000100001…

Source: NCERT CLASS 9 Maths Chapter 1 Exercise 1.3 Question 9

(i) Root of 23

√23

√23 = √23/1 = p/q, however, p is not an integer.

Therefore √23 is an irrational number.

(ii) Root of 225

√225

√225 = 15/1 = p/q, in which p and q are integers and q ≠ 0.

Therefore,  √225 is a rational number.

(iii) 0.3796

It is a rational number because it is a terminating decimal number.

(iv) 7.478478...

7.478478… It is a rational number because it is a non-terminating recurring decimal, meaning the block of numbers 478 is repeating.

(v) 1.10100100010001…

1.10100100010001… It is an irrational number as it is a non-terminating and non-recurring decimal.