Simplify the following:
1/sqrt(2) + 1/sqrt(8)
sqrt(8) = sqrt(2^3) = 2 sqrt(2):
1/sqrt(2) + 1/(2 sqrt(2))
Rationalize the denominator. 1/sqrt(2) = 1/sqrt(2)×(sqrt(2))/(sqrt(2)) = (sqrt(2))/2:
(sqrt(2))/2 + 1/(2 sqrt(2))
Rationalize the denominator. 1/(2 sqrt(2)) = 1/(2 sqrt(2))×(sqrt(2))/(sqrt(2)) = (sqrt(2))/(2×2):
(sqrt(2))/2 + (sqrt(2))/(2×2)
2×2 = 4:
(sqrt(2))/2 + (sqrt(2))/4
Put each term in (sqrt(2))/2 + (sqrt(2))/4 over the common denominator 4: (sqrt(2))/2 + (sqrt(2))/4 = (2 sqrt(2))/4 + (sqrt(2))/4:
(2 sqrt(2))/4 + (sqrt(2))/4
(2 sqrt(2))/4 + (sqrt(2))/4 = (2 sqrt(2) + sqrt(2))/4:
(2 sqrt(2) + sqrt(2))/4
2 sqrt(2) + sqrt(2) = 3 sqrt(2):
(3 sqrt(2))/4
