Suppose that the polynomial x^2+y^2-1 is not irreducible.
It means that there exists two fractions such that :

We found that q divide t and q divide s, but s and t are supposed to be prime each other. It is a contradiction.
The polynomial x^2+y^2-1 is then irreducible in q[x,y]
So, that's

*Helpful To Know
![{5}^{ \frac{1}{2} } = \sqrt{5} \\ {5}^{ \frac{1}{3} } = \sqrt[3]{5} \\ {5}^{ \frac{1}{4} } = \sqrt[4]{5} \\ {5}^{ \frac{3}{2} } = \sqrt{ {5}^{3} } \: \: or \: {( \sqrt{5} )}^{3}](https://tex.z-dn.net/?f=%7B5%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%3D%20%20%5Csqrt%7B5%7D%20%5C%5C%20%20%7B5%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%20%3D%20%20%5Csqrt%5B3%5D%7B5%7D%20%20%5C%5C%20%7B5%7D%5E%7B%20%5Cfrac%7B1%7D%7B4%7D%20%7D%20%20%3D%20%20%5Csqrt%5B4%5D%7B5%7D%20%20%20%20%5C%5C%20%20%20%7B5%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20%20%3D%20%20%5Csqrt%7B%20%7B5%7D%5E%7B3%7D%20%7D%20%5C%3A%20%20%5C%3A%20or%20%5C%3A%20%20%20%7B%28%20%5Csqrt%7B5%7D%20%29%7D%5E%7B3%7D%20)
----------------------------------------------------------------
*Assuming that you want to covert to radicals
![( \sqrt{8} )( \sqrt{x} )( \sqrt[4]{ {y}^{3} } )](https://tex.z-dn.net/?f=%28%20%5Csqrt%7B8%7D%20%29%28%20%5Csqrt%7Bx%7D%20%29%28%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B3%7D%20%7D%20%29)
*Simplify
Answer:
192
Step-by-step explanation:
Answer:
let this happens after t hours
so
80t + 60t = 392
140 t = 392
t = 392/140
=2.8 hours