1. Find six rational and six irrational number between 2/3 and 5/7

Asked by Jayant1142005 | 6th Apr, 2019, 03:05: PM

Expert Answer:

(2/3) = 0.666...
 
(5/7) ≈ 0.714
 
hence 6 rational numbers  between (2/3) and (5/7) in decimal form :  0.67 ,  0.68, 0.69, 0.7, 0.705, 0.71
 
or in fraction form :  67/100  , 17/25,  69/100, 7/10, 705/1000, 71/100
 
to get 6 irrational numbers between 2/3  and 5/7, we use the irrational numbers √2, √3, √5, √6, √7 and √8
after multiplying suitable fraction so that product of fraction and this irrational number is in between 2/3 and 5/7
 
hence 6 irrational numbers between 2/3 and 5/7 : √2/2 ,   2√3/5,  11√5/35,  11√6/40,  13√7/50  and √8/4 

Answered by Thiyagarajan K | 6th Apr, 2019, 05:27: PM

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