Question

prove that 3+2root 5 is irrational proceed with justifying root 5 is irrational

Answer 1

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Answer 2

Answer:

3 + 2√5

Step-by-step explanation:

Assume that 3+2  

root  5

​  

 is rational. Then,

3+2  

5

​  

=  

b

a

​  

 

5

​  

=  

2b

a−3b

​  

 

This gives that  

2b

a−3b

​  

 is rational but  

root 5

​  

 is an irrational number, therefore, the assumption is wrong.

Hence, 3+2  

root 5

​  

 is irrational.