wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Show that 5 + 5 is an irrational number.

Open in App
Solution


Let us assume that 5+5 is a rational number.

Then, 5+5 = ab, where a and b are co-prime integers (b0).
So,
5+5=abOr, 5=ab-5Or, 5=a-5bbSince a and b are integers, a-5bb is a rational number. So, 5 is a rational number. But this contradicts the fact that 5 is an irrational number.This contradiction arsies because of our wrong assumption that 5+5 is a rational number.So, 5+5 is an irrational number.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Revisiting Irrational Numbers
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon