wiz-icon
MyQuestionIcon
MyQuestionIcon
11
You visited us 11 times! Enjoying our articles? Unlock Full Access!
Question

State: True or False
3+25 is an irrational number.

A
True
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
False
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A True
Let us assume, to the contrary, that 3+25 is rational.

That is, we can find coprime integers a and b (b does not equal to 0) such that 3+25=ab.
Therefore, ab3=25
a3bb=25
a3b2b=5
a2b32=5
Since a and b are integers and rational, we get a2b32 is rational, and so a3b2b=5 is rational.

But this contradicts the fact that 5 is irrational.

This contradiction has arisen because of our incorrect assumption that 3+25 is rational.
So, we conclude that 3+25 is irrational.

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