Answer:
[tex]A=8\\\\B=7[/tex]
Step-by-step explanation:
Simplify the radicand by splitting the number into two numbers, one of which is a perfect square (like 4, 9, 16, 25, 36, 49, 64, 81, 100*).
Factors of 448 that include a perfect square: 7 and 64**. Split:
[tex]\sqrt{448} \\\\\sqrt{64*7}\\\\\sqrt{64}*\sqrt{7}\\\\ 8\sqrt{7}[/tex]
Therefore, A is 8 and B is 7.
:Done
Notes:
*Perfect squares:
[tex]\sqrt{4} =2\\\\\sqrt{9}=3\\\\\sqrt{16}=4\\\\\sqrt{25}=5\\\\\sqrt{36}=6[/tex] [tex]\sqrt{49}=7\\\\\sqrt{64}=8\\\\\sqrt{81}=9\\\\\sqrt{100} =10[/tex]
Make sure to use the number in the radical symbol, not the simplified number.
**You can find factors with a perfect square by dividing the radicand by perfect squares. The bigger the number, the better. I started at 100:
448÷100=4.48
448÷81=5.530864197
448÷64=7
Stop when you find one that results in a whole number, like 7. The result and perfect square are the factors.
