A perfect square must be hidden within all of those radicands in order to simplify them down to what the answer is.
![√(192)= √(64*3)= 8√(3)](https://img.qammunity.org/2019/formulas/mathematics/high-school/9v6ekprwxzkv2dmhvemwjkihh21inxush5.png)
.
![√(80)= √(16*5)=4 √(5)](https://img.qammunity.org/2019/formulas/mathematics/high-school/wfw6goyirlckma81294ypwizxkt7nhjtn2.png)
.
![√(12288)= √(4096*3)=64 √(3)](https://img.qammunity.org/2019/formulas/mathematics/high-school/r176sin3t55tkbrg6u6o4hsb3am461hg5d.png)
. The rules for adding radicals is that the index has to be the same (all of our indexes are 2 since we have square roots), and the radicands have to be the same. In other words, we cannot add the square root of 4 to the square root of 5. They either both have to be 4 or they both have to be 5. So here's what we have thus far:
![8 √(3)+4 √(5)+64 √(3)](https://img.qammunity.org/2019/formulas/mathematics/high-school/28nimklxmw36orev4jmjinxl829rnasz1u.png)
. We can add
![8 √(3)](https://img.qammunity.org/2019/formulas/mathematics/high-school/gjm096v1ydunejn03olghn5dz6hiohs8v4.png)
and
![64 √(3)](https://img.qammunity.org/2019/formulas/mathematics/high-school/75r04arrd4rzqv7x3f9afsobejj7zm89f5.png)
to get
![72 √(3)](https://img.qammunity.org/2019/formulas/mathematics/high-school/m1qg79gey93gevn75mimxcw5581hii22rc.png)
. That means as far as our answer goes, A = 72 and B = 4, or (72, 4), choice a.