Question

Prove that
3√3/5 is irrational.
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Answer 1

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Answer 2

Let √3 + √5 be a rational number , say r

then √3 + √5 = r

On squaring both sides, 

(√3 + √5)2  = r2 

3 + 2 √15 + 5 =  r2  

8 + 2 √15  = r2   

2 √15 =  r2  - 8 

√15 = (r2 - 8) / 2 

Now (r2 - 8) / 2 is a rational number and √15 is an irrational number . 

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