Question

given that √2 is irrational,prove that (5+3√2) is an irrational number

Answer 1

Heya☺

Let 5+3√2 be a rational no. then 5+3√2 = P/q where P and q are integers and co-prime numbers and q is not equal to 0

5+3√2 = P/q
√2 =( P/q -5)× 1/3

Here P/q , -5 , 1/3 are all integers and hence rational no.too this means √2 is also a rational no.

But this contradicts with the fact that √2 is an irrational no.
Hence our supposition was wrong

5+3√2 is an irrational no.
Hence proved

✌✌Hope this helps u❕