Question

Radicals and complex numbers

Answer 1

Answer:

$A=8\\\\B=7$

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:

$\sqrt{448} \\\\\sqrt{64*7}\\\\\sqrt{64}*\sqrt{7}\\\\ 8\sqrt{7}$

Therefore, A is 8 and B is 7.

:Done

Notes:

*Perfect squares:

$\sqrt{4} =2\\\\\sqrt{9}=3\\\\\sqrt{16}=4\\\\\sqrt{25}=5\\\\\sqrt{36}=6$         $\sqrt{49}=7\\\\\sqrt{64}=8\\\\\sqrt{81}=9\\\\\sqrt{100} =10$

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.