prove that 3+Root5 is irrational number
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Answered by
0
Answer:
as p, q and 3 are integers p-3q/3 is a rational number. =>root 5 is a rational number. ... this contradiction has arisen because of our wrong assumption that 3+root 5 is a rational number. hence 3+ root 5 is an irrational number.
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Answered by
1
Answer:
Let us assume that 3+
5
is a rational number.
Now,
3+
5
=
b
a
[Here a and b are co-prime numbers]
5
=[(
b
a
)−3]
5
=[(
b
a−3b
)]
Here, [(
b
a−3b
)] is a rational number.
But we know that
5
is an irrational number.
So, [(
b
a−3b
)] is also a irrational number.
So, our assumption is wrong.
3+
5
is an irrational number.
Hence, proved
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