prove that root 5-root 3 is not a rational number .
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2
Answer:
Let √(5) - √(3) be a rational number of form a/b ,where b≠ 0 Squaring on both sides (√(5) - √(3))^2 = (ab)^2 (√(5))^2 + (√(3))^2 - 2(√(5))(√(3 ... More
Answered by
1
Answer:
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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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