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Prove that 5sqrt(7) is irrational....

Prove that `5sqrt(7)` is irrational.

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Let if possible `5sqrt(7)` is rational.
Now, `5sqrt(7)` is rational and `(1)/(5)` is rational.
We know that the product of two rational numbers is rational.
`therefore` `5sqrt(7) xx (1)/(5)` is rational.
`rArr` `sqrt(7)` is rational.
But square root of prime number is always an irrational number. This contradicts the fact because an irrational number cannot be equal to rational number.
So, our supposition is wrong.
Hence, `5sqrt(7)` is irrational. Hence Proved.
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