Question

prove that ✓5 is irrational number ?​

Answer 1

Answer:

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2. A machine on an average manufacture 2,825 screws a day how

many screws did it produce in the month of January 2006?

3. The school canteen charges Rs.20 for lunch & Rs.4 for milk for

each day how much money do you spend in 5 days on these

things?

4. A vendor supplies 32L of milk to hotel in the morning & o8L of

milk in the evening if the milk costs Rs 45 per litres How much

money is due to vendor per day?

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Answer 2

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

Step-by-step explanation:

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