Math, asked by HACKERDIPESH, 9 months ago

. Prove that √5 is irrational.​

Answers

Answered by ssukhpuri
0

Answer:

............................

Answered by Anonymous
13

\huge \red{\bf Answer}

We need to prove that √5 is irrational

 \pink{\rm Proof:}

Let us assume that √5 is a rational number.

Sp it t can be expressed in the form p/q where p,q are co-prime integers and q≠0

⇒√5=p/q

On squaring both the sides we get,

⇒5=p²/q²

⇒5q²=p² —————–(i)

p²/5= q²

So 5 divides p

ANSWER

p is a multiple of 5

⇒p=5m

⇒p²=25m² ————-(ii)

From equations (i) and (ii), we get,

5q²=25m²

⇒q²=5m²

⇒q² is a multiple of 5

⇒q is a multiple of 5

Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

\green{ \bf \sqrt{5} \: is \:  a \: irrational \: number}

Similar questions