2√18 - 2√12 + 2√18 = A) 6√2 - 4√3 B) 12√2 - 4√3 C) 6√2 D) 12√2
2 answers:
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Answer:
The volume of the prism is
Step-by-step explanation:
we know that
The volume of the prism is equal to
where
B is the area of the triangular base
L is the length of the prism
we have
<em>Find the area of the base B</em>
The area of a equilateral triangle is equal to
substitute
1. We can conclude that the result of the division is 
with a remainder of 
, or in other notation: 
. Check the steps in the first image.
3. We can conclude that the result of the division is
with a remainder of 2, or in other notation: 
. Check the steps in the firts image.
5. We can conclude that the result of the division is
with a remainder of 5, or in other notation: 
. Check the steps in the first image.
7. To check if
is a factor of 
, we are going to perform long division. If the result of the long division has no remainder, is a factor of .
Since the result of the long division has no remainder, we can conclude that is a factor of . Check the steps in the second image.
9. To check if
is a factor of , we are going to perform long division. If the result of the long division has no remainder, 
is a factor of .
Since the result of the long division has no remainder, we can conclude that is a factor of . Check the steps in the third image.
10. We can conclude that the result of the synthetic division is
. Check the steps in the fourth image.
3. We can conclude that the result of the division is
5. We can conclude that the result of the division is
7. To check if
Since the result of the long division has no remainder, we can conclude that
9. To check if
Since the result of the long division has no remainder, we can conclude that
10. We can conclude that the result of the synthetic division is
2 ways: make a little divide tree based on how many times you can divide it. Like you have sqrt88 you know it can divide by 2. So its 2 and 44, and 44 can be broken to 2 and 22, then 2 and 11. 11 can’t be divided anymore.
Now choose numbers that are the same and pair them together. These go outside the radicand. You had three 2’s and one 11. So a 2 would go on the outside and the remaining 2 and 11 would be multiplied leaved 2sqrt22.
Another way is to divide by the highest squared number. Taking sqrt88 again. 4 would be the highest squared number. So 88 would be 4 and 22, then 2 and 11. Since you have a 4 which is a perfect square you put that squareroot outside. The inside would remain the same because it wouldn’t break down into perfect squares or pairs anymore. So that would be 2sqrt22.
Now choose numbers that are the same and pair them together. These go outside the radicand. You had three 2’s and one 11. So a 2 would go on the outside and the remaining 2 and 11 would be multiplied leaved 2sqrt22.
Another way is to divide by the highest squared number. Taking sqrt88 again. 4 would be the highest squared number. So 88 would be 4 and 22, then 2 and 11. Since you have a 4 which is a perfect square you put that squareroot outside. The inside would remain the same because it wouldn’t break down into perfect squares or pairs anymore. So that would be 2sqrt22.