## Given that root 2 is irrational prove that ( 5-3 root2) is an irrational number

Question

Given that root 2 is irrational prove that ( 5-3 root2) is an irrational number

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1 month 2021-08-18T11:14:15+00:00 1 Answer 0 views 0

1. Let 5-3√2 be a rational number r

5-3√2=r

-3√2=r-5

√2=(r-5)/-3

As, r is a rational no. so √2 should also be a rational number.

But we know that √2 is an irrational no.

Thus r is an irrational no.

Thus 5-3√2 is an irrational no.