Question

prove that 5 plus 7 root 2 is irrational

Answer 1

Solution:

Let us assume (5+7√2) is a rational number.

5+7√2 = a/b

Where , a,b are integers and

b≠0

=> 7√2 = a/b - 5

=> 7√2 = (a-5b)/b

=> √2 = (a-5b)/7b

Since , a,b are integers,

(a-5b)/7b is a rational .So , √2 is rational .

But ,this contradicts the

fact that √2 is an irrational.

Therefore,

5+7√2 is an irrational number.

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