How to find hcf by division method if there are 3 numbers
Answers
Answer:
Solution
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Suppose for the sake of contradiction that
3
is rational
We know that rational numbers are those numbers which can be expressed in
q
p
form ,where p and q are integers and q
=0
⟹
3
=
q
p
Squaring on both sides
3=
q
2
p
2
⟹p
2
=3q
2
∵p
2
is a multiple of 3⟹p must be a multiple of 3
let p=3n⟹p
2
=9n
2
⟹q
2
=3n
2
This means q is also a multiple of 3,which contradicts the fact that p and q had no common factor
Hence
3
is an irrational number
Suppose for the sake of contradiction that
5
is rational
We know that rational numbers are those numbers which can be expressed in
q
p
form ,where p and q are integers and q
=0
⟹
5
=
q
p
Squaring on both sides
5=
q
2
p
2
⟹p
2
=5q
2
∵p
2
is a multiple of 5⟹p must be a multiple of 5
let p=5n⟹p
2
=25n
2
⟹q
2
=5n
2
This means q is also a multiple of 5,which contradicts the fact that p and q had no common factor
Hence
5
is an irrational number
Step-by-step explanation: