Question

show that 7√5 is irrational
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Answer 1

Let us assume, to the contrary, that 7-√5 is rational

That is, we can find Coprime a and b (b≠ 0) such that

7-√5 = a/b

Therefore, 7 - a/b = √5

Rearranging this equation √5 = (7b -a)/b

since a and b are integers,so (7b -a)/b is an rational.

And so √5 is rational

But this contradicts the fact that √5 is irrational.

This contradiction has arisen because of our incorrect assumption that 7-√5 is rational.

Therefore we can conclude that 7-√5 is irrational.

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Hope it will be helpful :)

Answer 2

Answer:

Hence 75 can be written in the form of ba where a,b(b=0) are co-prime

⟹75=ba

⟹5=7ba

But here 5 is irrational and 7ba is rational

as Rational=Irrational

This is a contradiction 

so 75 is a irrational number