prove that is irrational
Answers
Answered by
0
Step-by-step explanation:
because √5 can't get any no.
Answered by
0
Let root 5 be a rational number where a and b are co primes where b Is not equal to 0.
Root 5 =a/b
Root5b=a
Squaring both sides
5b^2=a^2
Then 5 is a factor of a
Let a 5c for some integer c
Then
5b^2=(5c)^2
5b^2=25c^2
Then 5 is a factor of b
So a and b have 5 as a common factor,
But this contradicts the fact that a and b are co prime ,
This contradiction has arisen because of taking root 5 as rational,
So therefore root 5 is irrational
Root 5 =a/b
Root5b=a
Squaring both sides
5b^2=a^2
Then 5 is a factor of a
Let a 5c for some integer c
Then
5b^2=(5c)^2
5b^2=25c^2
Then 5 is a factor of b
So a and b have 5 as a common factor,
But this contradicts the fact that a and b are co prime ,
This contradiction has arisen because of taking root 5 as rational,
So therefore root 5 is irrational
Similar questions
Math,
3 months ago
Science,
3 months ago
Chemistry,
3 months ago
Science,
1 year ago
Social Sciences,
1 year ago