Question

find two irrational numbers between root 3 and root 5.

Answer 1

Hey friend, Harish here.

Here is your answer:

We know that:

√3 = 1.7320..........

√5 =2.2360.............

So,Two irrational numbers between them are:

1.75755755575555............

& 

2.10100100010000...........

These are two irrational numbers between.√3 & √5. But there are many.
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Hope my answer is helpful to you.

Answer 2

(3√3   +  √5)/4  ,  (√3   +  √5)/2  ,  (√3   +  3√5)/4  are irrational number between √3   &  √5

Step-by-step explanation:

irrational number between √3   &  √5 = (√3   +  √5)/2

√3 <  (√3   +  √5)/2 <  √5

Further irrational number

(√3 +  (√3   +  √5)/2)/2  =  (3√3   +  √5)/4

and

( (√3   +  √5)/2 +  √5)/2  = (√3   +  3√5)/4

√3 <  (3√3   +  √5)/4  < (√3   +  √5)/2  <  (√3   +  3√5)/4<  √5

(3√3   +  √5)/4  ,  (√3   +  √5)/2  ,  (√3   +  3√5)/4  are irrational number between √3   &  √5

Another method

irrational number between √3   &  √5

squaring both  3  5

(3 + 5)/2 = 4  but perfect square

(3 + 4)/2 = 7/2   & (4 + 5)/2 = 9/2

√(7/2)  & √(9/2)  are  Rational number between √3   &  √5

Learn more:

insert 5 irrational number between 2 root 5 and 3 root 3 - Brainly.in

https://brainly.in/question/7810457