-1/√5 is a rational number
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5 is a rational number because it can be expressed as the quotient of two integers: 5 ÷ 1.
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Answer:
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Step-by-step explanation:
Let us assume that
5
1
be a rational number.
Then, it will be of the form
b
a
wher a and b are co-prime and b
=0.
Now,
b
a
=
5
1
⇒
b
a
=
5∗
5
1∗
5
⇒
b
5a
=
5
Since, 5a is an integer and b is also an integer.
So
b
5a
is a rational number.
⇒
5
is a rational number.
But this contradicts to the fact that
5
is an irrational number.
Therefore, our assumption is wrong.
Hence,
5
1
is an irrational number.
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