1.

Prove that√5 is irrational​

Answer»

Answer & Step-by-step explanation:

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/q

On squaring both the sides we get,

⇒5 = p²/q²

⇒5q² = p² —————–(i)

p²/5 = q²

So 5 divides p

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.

√5 is an IRRATIONAL number.


Discussion

No Comment Found

Related InterviewSolutions