Question

Need help please !!!!!!

Answer 1

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