Question

Prove that (2-√7) is an irrational number, given that√7 is irrational
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Answer 1

It is always irrational in this case

Answer 2

Let us assume that 2/√7 is rational number.

2/√7= 2/√7 × (√7/√7)= 2√7/7. ( Rationalising)

Now, 2√7/7 = p/q ( as rational no. can be written in the form of p/q=)

2√7= 7p/q

√7= 7p/2q

Here LHS is irrational but RHS is rational.

This contradicts the statement.

Our assumption is wrong.

2/ √7 is an irrational number.