Question

Prove that (2 - √5) is an irrational number.​

Answer 1

Answer:

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.

Answer 2

Solution -

Let us assume (2 - √5) is a rational number.

$(2 - \sqrt{5}) = \frac{p}{q}$

Where p and q € z, q ≠ 0

$2 - \frac{p}{q} = \sqrt{5}$

$\frac{2q - p}{q} = \sqrt{5}$

➜ √5 is a rational number.

$∵ \frac{2q - p}{q} \: is \: a \: rational \: number \:$

But √5 is not a rational number.

Therefore, our supposition 2 - √5 is a rational number is wrong.

➜ 2 - √5 is an irrational number.

ﾟ･*☆¸¸.•*¨*•♪¸¸.•*¨*•.•*¨*•.¸¸☆*･ﾟ

➻❥Iռɕɾεɖıɓɭε Kɦυꜱɦı࿐ཽ༵