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प्रश्न
Prove that the following is irrational:
`7sqrt5`
उत्तर
Let a = `7sqrt5` be a rational number.
We can find two co-prime integers a and b such that `7 sqrt5 = a/b` Where b ≠ 0
Now, `7 sqrt5 = a/b`
⇒ `a/(7b) = sqrt5.`
Now, `a/7` is a rational number since the product of two rational numbers is a rational number.
The above will imply that `sqrt5` is a rational number. But `sqrt5` is an irrational number.
∴ Our assumption is wrong.
Thus, we conclude that `7 sqrt5` is irrational.
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