Question

Suppose the total length of the truck and trailer is given by the expression 8 √ 50 . If the trailer measures 7 √32 , which radical expression represents the remaining length for the truck's cab? A) 10 √ 2 B) 12 √ 2 C) 8 √ 4 D) √ 18

Answer 1

Answer:

B

Step-by-step explanation:

To find out the length of the truck's cab, you subtract the length of the trailer from the whole length of the truck.  However, this cannot be done with the radicals as they are.  In order to add or subtract radicals, not only does the index have to be the same (here they are the same; both are square roots), the radicands (the numbers under the radical) also have to be the same and they are not.  Let's see if we can manipulate them into being the same by simplifying each.  50 is the same as 25*2, and 32 is the same as 16*2:

8√25*2 = 40√2

7√16*2 = 28√2

Now that the radicands are the same we can subtract them:

$40\sqrt{2}-28\sqrt{2}=12\sqrt{2}$