Question

Prove that 3/root5 is irrational​

Answer 1

Answer:

the value of 3/√5 = 1.3416....

An irrational number is a number that can't be expressed as a fraction for any integers and these numbers have decimal expansions that neither terminate nor become periodic.

So it is a irrational number.

Hence Proved.

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Answer 2

Hey!!! Here is your answer......

Lets assume 3√5 is a rational number.

3√5 = a/b (where b≠0)

3= a/b -√5

Squaring on both sides....

(3)²= [a/b-√5]

9 = a²/b²+5 -2(a/b) (√5)

(since (a-b) ²= a²+b²-2ab)

Rearranging.....

2a/b √5 = a²/b²-4

2a/ b √5 = a²-4b²/b²

√5 = a²-4b²/2ab

Here L. H. S = irrational number.

R. H. S = rational number.

An irrational number is not equal to rational number. Thus it contradicts the fact.

So, our assumption is wrong that 3√5 is a rational number.

:. 3√5 is an irrational number.

Hence proved..

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