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Simplify: $\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{8}}$.

 Aug 26, 2021
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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

 Aug 26, 2021

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