Question

Prove that there is no rational number whose square is 6.

Answer 1

Hello ♥️

The proof I am going to mention is copied:-
Let's assume that 12=(pq)12=(pq), where p,q ∈∈ RR and ppand qq are coprime.

Then we have,

(p2q2)=122=144.(p2q2)=122=144.

So,

p2=144∗q2p2=144∗q2

and p2=2∗(72)∗q2.p2=2∗(72)∗q2.

This implies that p is even.

Then,

p=(2k)p=(2k)

So,

(2k)2=2∗(72)∗q2(2k)2=2∗(72)∗q2

4k2=2∗(72)∗q24k2=2∗(72)∗q2

2k2=72q22k2=72q2

Thus,

k2=36q2k2=36q2

so,

k=6qk=6q

then (pq)=(12qq)(pq)=(12qq),

which contradicts p and q being coprime. Therefore 12 is irrational. QED

I hope this is helpful ♥️
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Answer 2

Hey frnd..
Gud morning...

ur answer is in the attachment...

hope it helps..
plzz mark me as brainliest my dear !!!