Question

Prove that 2-root 5 is an irrational number..
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Answer 1

you have to prove 1st that root5 is irrational then

rational-irrational = irrational

Answer 2

Step-by-step explanation:

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

2+5=qp where p,q∈z,q=0

2−qp=−5

q2q−p=−5

⇒−5 is a rational number

∵q2q−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 number.