10. Prove u11. Prove thatis irrationalISED)

1.	10. Prove u11. Prove thatis irrationalISED)
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.

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.

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