Question

prove that 3-√5 is an irrational number​

Answer 1

Step-by-step explanation:

Let

3 - √5 be a rational number

.°. 3 + √5 = p/q [ where p and q are integer , q ≠ 0 and q and p are co - prime number ]

=> √5 = p/q - 3

=> √5 = p - 3q/q

we know that p/q is a rational number.

.°. √5 is also a rational number.

This contradicts our assumption.

.°. 3 - √5 is an irrational number.

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