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Ncert exemplar solutions

A rational number between 2 and 3 is

(A) (√2+√3)/2

(B) (√2. √3)/2

(C) 1.5

(D) 1.8

(C) 1.5

Explanation:

√2 =1.4142135.... and √3 =1.732050807....

(A) (√2+√3)/2 = 1.57313218497… is a non-terminating and non-recurring decimal and therefore is an irrational number.

(B) (√2. √3)/2 = 1.22474487139… is a non-terminating and non-recurring decimal and therefore is an irrational number.

(C) 1.5 is a terminating decimal and therefore is a rational number.

(D) 1.8 is a terminating decimal and therefore is a rational number.

Here both 1.5 and 1.8 are rational numbers. But, 1.8 does not lie in between √2 =1.4142135.... and √3 =1.732050807....

Whereas 1.5 lies in between √2 =1.4142135.... and √3 =1.732050807....

Hence, (C) is the correct option.

A rational number between 2 and 3 is

(A) (√2+√3)/2

(B) (√2. √3)/2

(C) 1.5

(D) 1.8

(C) 1.5

Explanation:

√2 =1.4142135.... and √3 =1.732050807....

(A) (√2+√3)/2 = 1.57313218497… is a non-terminating and non-recurring decimal and therefore is an irrational number.

(B) (√2. √3)/2 = 1.22474487139… is a non-terminating and non-recurring decimal and therefore is an irrational number.

(C) 1.5 is a terminating decimal and therefore is a rational number.

(D) 1.8 is a terminating decimal and therefore is a rational number.

Here both 1.5 and 1.8 are rational numbers. But, 1.8 does not lie in between √2 =1.4142135.... and √3 =1.732050807....

Whereas 1.5 lies in between √2 =1.4142135.... and √3 =1.732050807....

Hence, (C) is the correct option.

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