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Number Systems | Number Systems - Exercise 1.1

Question 19

A rational number between √2 and √3 is ___________>

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√2 =1.4142135…. and √3 =1.732050807….

(A) \frac{(\sqrt{2}+\sqrt{3})}{2} = 1.57313218497… is a non-terminating and non-recurring decimal and therefore is an irrational number.

(B) \frac{(\sqrt{2}.\sqrt{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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Question 19

A rational number between √2 and √3 is ___________>

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

√2 =1.4142135…. and √3 =1.732050807….

(A) \frac{(\sqrt{2}+\sqrt{3})}{2} = 1.57313218497… is a non-terminating and non-recurring decimal and therefore is an irrational number.

(B) \frac{(\sqrt{2}.\sqrt{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.

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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