Prove that √5 is a is an irrational number. Question Prove that √5 is ais an irrational number. in progress 0 Math Clara 2 days 2021-10-12T06:25:01+00:00 2021-10-12T06:25:01+00:00 2 Answers 0 views 0

## Answers ( )

Answer:2.236…….

Step-by-step explanation:this is the ans because the no goes on so we can’t make it as rational number so it’s irrational number.

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

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

Hence proved

hope it will help u….