Classify the following numbers as rational or irrational.(i) 2 - √5(

1.	Classify the following numbers as rational or irrational.(i) 2 - √5(ii) (3 + √23) - √23(iii) (2√11)/(7√11)(iv) 1/√3(v) 2π
Answer» (i) 2 – √5 is an irrational number. (ii) (3 + √23) – √23 = 3 + √23 – √23 = 3 Hence, it is a rational number. \(\frac { 2\sqrt { 11 } }{ 7\sqrt { 11 } } =\frac { 2 }{ 7 } \) Hence, it a rational number. (iv) \(\frac { 1 }{ \sqrt { 3 } } \) is an irrational number. (v) 2π is an irrational number.

Classify the following numbers as rational or irrational.(i) 2 - √5(ii) (3 + √23) - √23(iii) (2√11)/(7√11)(iv) 1/√3(v) 2π

Answer»

(i) 2 – √5 is an irrational number.

(ii) (3 + √23) – √23

= 3 + √23 – √23 = 3

Hence, it is a rational number.

\(\frac { 2\sqrt { 11 } }{ 7\sqrt { 11 } } =\frac { 2 }{ 7 } \)

Hence, it a rational number.

(iv) \(\frac { 1 }{ \sqrt { 3 } } \) is an irrational number.

(v) 2π is an irrational number.