Question

prove that 2-√5 is an irrational number

Answer 1

Solution:

Let us assume (2-√5) is a

rational.

2-√5 = a/b , where a,b are

integers and b ≠ 0.

=> √5 = 2-a/b

=> √5 = (2b-a)/b

Since , a,b are integers (2b-a)/b

is a rational ,so, √5 is rational.

But it contradicts the fact that √5 is irrational.
This contradiction has arisen because of our
incorrect assumption
that 2-√5 is rational.

Therefore,

So, we conclude that 2-√5 is irrational.

••••

Answer 2

Answer:

Step-by-step explanation:

√5 is an irrational number

- √5 is an irrational number

2 is a rational number

sum of  an irrational number and  a irrational number  is an irrational number

so    - √5 +2 is an irrational

2-√5 is an irrational number