Question

find ratinoal number between 3/2√3 and 5/2√3
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Answer 1

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A rational number between 2/3 and 3/5 is 1/2 (2/3 + 3/5) = 1/2( [10+9]/15 ) = 1/2(19/15) = 19/30

Then, 2/3 < 19/30 < 3/5

A rational number between 2/3 and 19/30 = 1/2 {2/3 + 19/30} = 1/2 ([20+19]/30) = 1/2(39/30) = 39/60

A rational number between 19/30 and 3/5 = 1/2 {19/30 + 3/5} = 1/2 ([19+18]/30) = 1/2(37/30) = 37/60

Therefore, 2/3 < 39/60 < 19/30 < 37/60 < 3/5

Hence, 39/60, 19/30 and 37/60 are the three rational numbers lying between 2/3 and 3/5. 

Answer 2

Hello friends

I am here to help you

A rational number between 2/3 and 3/5 is 1/2 (2/3 + 3/5) = 1/2( [10+9]/15 ) = 1/2(19/15) = 19/30

Then, 2/3 < 19/30 < 3/5

A rational number between 2/3 and 19/30 = 1/2 {2/3 + 19/30} = 1/2 ([20+19]/30) = 1/2(39/30) = 39/60

A rational number between 19/30 and 3/5 = 1/2 {19/30 + 3/5} = 1/2 ([19+18]/30) = 1/2(37/30) = 37/60

Therefore, 2/3 < 39/60 < 19/30 < 37/60 < 3/5

Hence, 39/60, 19/30 and 37/60 are the three rational numbers