Question

prove that 3-√5 is irrational​

Answer 1

Answer:

3 - √5 is an irrational number.

Step-by-step explanation:

Let us assume that 3−√5 is a rational number

Then, there exist coprime integers p, q, q not equal to 0 such that

3−√5 = p/q

=> 5=3−qp

Here,  3 - p/q is a rational number, but √5 is an irrational number.

But, a irrational cannot be equal to a rational number.

This is a contradiction.

Thus, our assumption is wrong.

Therefore 3−√5 is an irrational number.

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