prove that 5-3/root2
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Answer:
Given that
2
is irrational.
We know that the theorem "The product of any irrational number with a rational number is irrational".
So, since we know 3 is a rational number, 3
2
is irrational.
(3=
1
3
;1
=0)
Now we know that 3
2
is irrational.
Theorem: The sum of a rational number with an irrational number is irrational.
So, since we know 5 is a rational number, 5+3
2
is irrational.
(5=
1
5
;1
=0)
Thus we proved that 5+3
2
is an irrational number.
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