Question

show that 2+√7 is irrational

Answer 1

Hi friend, Here's the required answer:-

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.

Hope this helps you...

All the best….

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.
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