Question

Prove that √5 is irrational number​

Answer 1

$\huge\mathfrak\pink{Answer}$

Let us assume that √5 is a rational number.

So it can be expressed in the form p/q where p,q are co-prime integers and q≠0⇒ √5 = p/qOn squaring both the sides we get,⇒5 = p²/q²⇒5q² = p² —————–(i)p²/5 = q²So 5 divides pp 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 5Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number√5 is an irrational number.

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Answer 2

Answer:

Irrational numbers are those who are not in form of p/q where p and q are not Integers and q is not equal to 0.

Step-by-step explanation:

√5 = 2.23606....

which is not in form of p/q where p and q are not Integers and q is not equal to 0