Abox of chocolates has 8 solid chocolates and 4 chocolate covered caramels. what is the ratio of chocolate covered caramels to solid chocolates?

1/2

Step-by-step explanation: We can write a ratio using the word "to," using a colon, or using a fraction bar. I would personally write the ratio using a fraction bar since it's easier to write in lowest terms.

So we need to compare the number of chocolate covered caramels to the number of solid chocolates.

We know that we have 4 chocolate covered caramels so we write 4 in the numerator of our ratio. We know that we have 8 solid chocolates so we put an 8 in the denominator of our ratio.

Now we have the fraction 4/8.

Notice however that 4/8 is not in lowest terms so we need to divide the numerator  and denominator by the greatest common factor of 4 and 8 which is 4 to get 1/2. So the ratio of the number of chocolate covered caramels to the number of solid chocolates is 1/2.

The given expression is in the form (a+b)(a-b) where
a = 5
b = sqrt(3)

Recall that 
(a+b)(a-b) = a^2-b^2
is the difference of squares formula

If a = 5, then a^2 = 25
If b = sqrt(3), then b^2 = (sqrt(3))^2 = 3
The squaring undoes the square root. The two opposites cancel out.

So using a^2 = 25 and b^2 = 3, we can say
(a+b)(a-b) = a^2-b^2 = 25-3 = 22

Therefore,
(5+sqrt(3))(5-sqrt(3)) = 22

B) 22