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What is the following quotient? 2- sqrt 8 / 4 + sqrt 12
4 months ago
Q:
What is the following quotient? 2- sqrt 8 / 4 + sqrt 12
Accepted Solution
A:
C is the answer.
We multiply the top and bottom of this by the conjugate (switch the sign of the square root):
(2-sqrt8)(4-sqrt12)/(4+sqrt12)(4-sqrt12)
Multiying the top we have
8-2sqrt12-4sqrt8+sqrt(8Γ12)
Multiplying the bottom we have:
16-4sqrt12+4sqrt12-12
On top, we simplify the radicals and get
8-4sqrt3-8sqrt2+4sqrt6
On bottom, we have
16-12=4
Now we divide everything on top by 4 and get
2-sqrt3-2sqrt2+sqrt6