Answer: Choice C) ![2-\sqrt{3}-2\sqrt{2}+\sqrt{6}\\\\\\](https://tex.z-dn.net/?f=2-%5Csqrt%7B3%7D-2%5Csqrt%7B2%7D%2B%5Csqrt%7B6%7D%5C%5C%5C%5C%5C%5C)
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Work Shown:
Part 1
![\frac{2-\sqrt{8}}{4+\sqrt{12}}\\\\\\\frac{(2-\sqrt{8})(4-\sqrt{12})}{(4+\sqrt{12})(4-\sqrt{12})}\\\\\\\frac{2(4-\sqrt{12})-\sqrt{8}(4-\sqrt{12})}{(4)^2-(\sqrt{12})^2}\\\\\\\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{8}*\sqrt{12}}{16-12}\\\\\\\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{8*12}}{4}\\\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B2-%5Csqrt%7B8%7D%7D%7B4%2B%5Csqrt%7B12%7D%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%282-%5Csqrt%7B8%7D%29%284-%5Csqrt%7B12%7D%29%7D%7B%284%2B%5Csqrt%7B12%7D%29%284-%5Csqrt%7B12%7D%29%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B2%284-%5Csqrt%7B12%7D%29-%5Csqrt%7B8%7D%284-%5Csqrt%7B12%7D%29%7D%7B%284%29%5E2-%28%5Csqrt%7B12%7D%29%5E2%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%5Csqrt%7B12%7D-4%5Csqrt%7B8%7D%2B%5Csqrt%7B8%7D%2A%5Csqrt%7B12%7D%7D%7B16-12%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%5Csqrt%7B12%7D-4%5Csqrt%7B8%7D%2B%5Csqrt%7B8%2A12%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C)
Part 2
![\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{96}}{4}\\\\\\\frac{8-2\sqrt{4*3}-4\sqrt{4*2}+\sqrt{16*6}}{4}\\\\\\\frac{8-2\sqrt{4}*\sqrt{3}-4\sqrt{4}*\sqrt{2}+\sqrt{16}*\sqrt{6}}{4}\\\\\\\frac{8-2*2*\sqrt{3}-4*2*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{8-4*\sqrt{3}-8*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B8-2%5Csqrt%7B12%7D-4%5Csqrt%7B8%7D%2B%5Csqrt%7B96%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%5Csqrt%7B4%2A3%7D-4%5Csqrt%7B4%2A2%7D%2B%5Csqrt%7B16%2A6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%5Csqrt%7B4%7D%2A%5Csqrt%7B3%7D-4%5Csqrt%7B4%7D%2A%5Csqrt%7B2%7D%2B%5Csqrt%7B16%7D%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%2A2%2A%5Csqrt%7B3%7D-4%2A2%2A%5Csqrt%7B2%7D%2B4%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-4%2A%5Csqrt%7B3%7D-8%2A%5Csqrt%7B2%7D%2B4%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C)
Part 3
![\frac{8-4*\sqrt{3}-8*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{4*2-4*1*\sqrt{3}-4*2*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{4(2-\sqrt{3}-2\sqrt{2}+\sqrt{6})}{4}\\\\\\2-\sqrt{3}-2\sqrt{2}+\sqrt{6}\\\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B8-4%2A%5Csqrt%7B3%7D-8%2A%5Csqrt%7B2%7D%2B4%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B4%2A2-4%2A1%2A%5Csqrt%7B3%7D-4%2A2%2A%5Csqrt%7B2%7D%2B4%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B4%282-%5Csqrt%7B3%7D-2%5Csqrt%7B2%7D%2B%5Csqrt%7B6%7D%29%7D%7B4%7D%5C%5C%5C%5C%5C%5C2-%5Csqrt%7B3%7D-2%5Csqrt%7B2%7D%2B%5Csqrt%7B6%7D%5C%5C%5C%5C%5C%5C)
This shows the answer is choice C.
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Explanation:
There are a lot of steps, so I broke things up into 3 sections or parts. The idea I'm applying is if the denominator is of the form
, then multiplying top and bottom by
will rationalize the denominator. This is due to the difference of squares rule (step 3 of part 1). The following step shows squaring a square root has the two cancel out.
From that point, I simplified each square root and factored to cancel out a pair of '4's.
To expand out
, we can use either the FOIL method, the box method, or the distribution property. I used the distribution property.
Answer:
15 and 5
Step-by-step explanation:
<u>15</u>:25::3:<u>5</u>
so, extreme are the terms which the underlined
Answer:
Distances:
A=1/2
B= 1
C= 3/2
Heights:
D= 1
E= 0
F= -1
Step-by-step explanation:
i just took the same quiz i hope this helped ;)
If he uses the same amount of water each day then that means its constant. So take your amount of given gallons and divide it by the amount of days there are. What's 645.6/7?
Y would equal 40 because 180 is the total