Answer:
5√5722 * 2√22
We can start by multiplying them since its a product.
10√115884
Well you have this now.
So whats the square root of 115884, not rational.
Well from here everything I did here was useless since it could be determined if the number is rational or irrational right away. Although you could solve like this, you’d get a decimal so irrational number.
One of the first hints you can notice here is that the square root of 22 is a decimal which is already irrational. Multiplying it by 2 doesnt help either. That helps since if the other number is irrational, its not always rational and in this case √5722 doesn’t fit in any perfect square root either.
Thats how to solve it.
Final answer: Irrational
