Question

prove that 5-2 root 3/7 is irrational number​

Answer 1

Let 5-2/7√3 be rational no.

therefore

5-2/7√3=p/q

(where p and q are co prime)

2/7√3=5-p/q

2/7√3=5q-p/q

√3=7(5q-p)/2q

here 7,5,2,q,and p are integers.

therefore 7(5q-p)/2q is rational

therefore √3 is rational no

but this contradicts the fact that √3 is irrational no

therefore 5-2/7√3 is irrational no.

hence proved

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