Simplify the following:
2/sqrt(12)-sqrt(8)
sqrt(12) = sqrt(2^2×3) = 2 sqrt(3):
2/2 sqrt(3)-sqrt(8)
2/(2 sqrt(3)) = 2/2×1/sqrt(3) = 1/sqrt(3):
1/sqrt(3)-sqrt(8)
sqrt(8) = sqrt(2^3) = 2 sqrt(2):
1/sqrt(3)-2 sqrt(2)
Rationalize the denominator. 1/sqrt(3) = 1/sqrt(3)×(sqrt(3))/(sqrt(3)) = (sqrt(3))/(3):
(sqrt(3))/(3)-2 sqrt(2)
Put each term in (sqrt(3))/(3)-2 sqrt(2) over the common denominator 3: (sqrt(3))/(3)-2 sqrt(2) = (sqrt(3))/(3)+(-6 sqrt(2))/(3):
(sqrt(3))/(3)+(-6 sqrt(2))/(3)
(sqrt(3))/(3)-(6 sqrt(2))/(3) = (sqrt(3)-6 sqrt(2))/(3):
Answer: | (sqrt(3)-6 sqrt(2))/(3)=1/sqrt(3)-2 sqrt(2)=- 2 sqrt(2) + 1/sqrt(3)
