Question

show that 3 + 7 root 2 is an irrational number ..
is the sum of two irrational number always irrational...

Answer 1

s sum of two irrational no. is always irrational.
take an example of underroot 2 and underroot 2 there sum comes out to be 2underoot 2
Assume thus no. To be rational no. shift 2 on RHS underroot 2 is irrational no.but p/2q is irrational no. and write the solution which I wrote in pic


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Answer 2

Answer:

Let us assume 3+7 √2 as rational number

3+7√2 =a\b

√2 = a/7b - 3

Here,

a/7b -3 is rational number so

3+7√2 is also rational number

But √2 is irrational

This contradiction had arrisen due to our incorrect assumption

This contradicts the fact that 3+7√2 is irrational

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