Question

Prove that 5 ÷3 root7 is an irrational number

Answer 1

Let us take on contrary that 3 root 7 is rational. then there exist two co prime numbers a and b such that 

3root 7 = a/b

=> root 7 = a / 7b

now LHS is an irrational no. whereas RHs is rational

this contradiction has arised due to our wrong assumption in beginning 

therefore 3 root 7 is an irrational number

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