Prove that underroot 7 is an irrational number
Answers
Answer:
I HOPE IT'S CORRECT ANSWER
Step-by-step explanation:
us assume that
7
is rational. Then, there exist co-prime positive integers a and b such that
7
=
b
a
⟹a=b
7
Squaring on both sides, we get
a
2
=7b
2
Therefore, a
2
is divisible by 7 and hence, a is also divisible by7
so, we can write a=7p, for some integer p.
Substituting for a, we get 49p
2
=7b
2
⟹b
2
=7p
2
.
This means, b
2
is also divisible by 7 and so, b is also divisible by 7.
Therefore, a and b have at least one common factor, i.e., 7.
But, this contradicts the fact that a and b are co-prime.
Thus, our supposition is wrong.
Hence,
7
is irrational.
Answered By
toppr
2052 Views
How satisfied are you with the answer?
This will help us to improve better
answr
Get Instant Solutions, 24x7
No Signup required
girl
More Questions by difficulty
EASY
MEDIUM
HARD
star
Related Questions to study
(2+
5
)(2+
5
) expression
i hope you understand
plz mark mark me as brainlist