A perfect square must be hidden within all of those radicands in order to simplify them down to what the answer is. [tex] \sqrt{192}= \sqrt{64*3}= 8\sqrt{3} [/tex]. [tex] \sqrt{80}= \sqrt{16*5}=4 \sqrt{5} [/tex]. [tex] \sqrt{12288}= \sqrt{4096*3}=64 \sqrt{3} [/tex]. 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: [tex]8 \sqrt{3}+4 \sqrt{5}+64 \sqrt{3} [/tex]. We can add [tex]8 \sqrt{3} [/tex] and [tex]64 \sqrt{3} [/tex] to get [tex]72 \sqrt{3} [/tex]. That means as far as our answer goes, A = 72 and B = 4, or (72, 4), choice a.
