Show that 2-√7 is irrational.

1.	Show that 2-√7 is irrational.
Answer» If we are known with √7 is irrational than it can be proved as: Let 2 - √7 be a rational number 2 - √7 = p/q [ where p and q are integer , q ≠ 0 and q and p are co-prime number ] => √7 = 2 - p/q => √7 = (2q - p)/q We know that number of form p/q is a rational number. from here, √7 is also a rational number. But we know that √7 is irrational number. This contradicts our assumption. Therefore, 3 - √5 is an irrational number.

Answer»

If we are known with √7 is irrational than it can be proved as:

Let 2 - √7 be a rational number

2 - √7 = p/q [ where p and q are integer , q ≠ 0 and q and p are co-prime number ]

=> √7 = 2 - p/q

=> √7 = (2q - p)/q

We know that number of form p/q is a rational number.

from here, √7 is also a rational number.

But we know that √7 is irrational number. This contradicts our assumption.

Therefore, 3 - √5 is an irrational number.

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Show that 2-√7 is irrational.

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