Prove that 3/ 2 root 5 is irrational number.

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Prove that if root 5 is irrational, then 3/2 root 5 is irrational. 

If 3/2 root 5 is rational, then root 5 is rational: 

3/2 root 5 = a / b 
root 5 = (2a) / (3b) 

Therefore, if root 5 is irrational, then 3/2 root 5 is irrational. 
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