prove that√5-√3 is not a rational number
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Answered by
2
Answer:
Answer. Assume that √3 + √5 = p/q (it's rational). Multiple both sides by (√5 - √3). √5 = [(p/q) + (2q/p)]/2, a rational number.
Answered by
2
Step-by-step explanation:
Let
5
−
3
be a rational number of form
b
a
,where b
=0
Squaring on both sides
(
5
−
3
)
2
=(
b
a
)
2
(
5
)
2
+(
3
)
2
−2(
5
)(
3
)=
b
2
a
2
5+3+2
1
5=
b
2
a
2
8+2
1
5=
b
2
a
2
2
1
5=
b
2
a
2
−8
1
5=
2b
2
a
2
−8b
2
since
1
5 is irrational ,
2b
2
a
2
−8b
2
is rational
Since LHS
= RHS, contradiction arises,
Therefore
5
−
3
is irrational
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