Question

Based on the understanding about personal social qualities , observe for a week your own self as you interact with*interaction can be on virtual platform) 1.your students in the classroom or 2.your school principal/colleague with whom you have been having conflict or 3.your children at home Reflect on where all you have put to practice the personal social qualities. Identify which quality was used and how you expressed it.How did you get to know that?Submit your daily observation with appropriate evidence to support your observation
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Answer 1

Explanation:

Question : Prove that√5 is irrational.

Answer :

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