Question

Prove that 2√3-7√2 is an irrational number

Answer 1

Solution:-

To Proof:-

(2√3-7√2) is an irrational number.

Proof :-

Let (2√3-7√2) be a Rational Number.

=) It can be written in the form of p/q. Where q is not equal to 0 & q and p are some Integer.

=) (2√3-7√2) = p/q

=) 2√3 - 7√2 = P/q

=) 2√3 = p/q + 7√2

=) √3 = ( p/q + 7√2)/2

Here,

( p/q + 7√2)/2 may be rational but we know that √3 is Irrational.

=) It Contradicts our supposition that (2√3-7√2) is a Rational Number.

Hence,

(2√3-7√2) is an Irrational Number.

Hence Proved!!