Question

Show that there is no rational number whose square is 3 ,5 6 7 12

Answer 1

Let's assume that 12=(pq), where p,q ∈ R and p and q are coprime.

Then we have,

(p2q2)=122=144.

So,

p2=144∗q2

and p2=2∗(72)∗q2.

This implies that p is even.

Then,

p=(2k)

So,

(2k)2=2∗(72)∗q2

4k2=2∗(72)∗q2

2k2=72q2

Thus,

k2=36q2

so,

k=6q

then (pq)=(12qq),

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

I hope it helps you

Please mark me Brainlist and follow me

Answer 2

Answer:

hope this helps u mate u have to just follow the same steps for other numbers...