Prove that ?7+3/2 is irrational
Dear Student,
Please find below the solution to the asked query:
Let + is a rational number .
Then we we can represent it in form of , where p and q are co-prime integers, So
+ =
- =
Now squaring both side ,we get
( - )2=
=
+ 7 - = 2
+ = 2
=
=
Hence
is a rational number .
But we know that is a irrational number , So that contradict fact that is a irrational number .
So,
Our assumption is incorrect ,
Hence + is a irrational number ( Hence proved )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Let + is a rational number .
Then we we can represent it in form of , where p and q are co-prime integers, So
+ =
- =
Now squaring both side ,we get
( - )2=
=
+ 7 - = 2
+ = 2
=
=
Hence
is a rational number .
But we know that is a irrational number , So that contradict fact that is a irrational number .
So,
Our assumption is incorrect ,
Hence + is a irrational number ( Hence proved )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards