Question

Prove That 2 - √5 is an irrational,where√5 is irrational​

Answer 1

Step-by-step explanation:

If possible, let us assume 2+ 5is a rational number.

∴ 2-√5 = p/q, where p,q are co-prime numbers,q is not equal to 0

=> 2 - p/q = √5

=> (2p - p)/ q = √5

=> -√5 is rational number

∵ (2p - p) / q is a rational number

But √5 is not a rational number

∴ Our supposition is incorrect and

=> 2 - √5 is irrational number

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Answer 2

Answer:

Step-by-step explanation:

If possible, let us assume 2+  

5

​  

 is a rational number.

2+  

5

​  

=  

q

p

​  

 where p,q∈z,q



=0

2−  

q

p

​  

=−  

5

​  

 

q

2q−p

​  

=−  

5

​  

 

⇒−  

5

​  

 is a rational number

∵  

q

2q−p

​  

 is a rational number

But −  

5

​  

 is not a rational number.

∴ Our supposition 2+  

5

​  

 is a rational number is wrong.

⇒2+  

5

​  

 is an irrational numb