obs23 wrote:

\((\sqrt{15+4\sqrt{14}}+\sqrt{15-4\sqrt{14}})^2\)

A. 28

B. 29

C. 30

D. 31

E. 32

We can let

x = √(15 + 4√14) and

y = √(15 - 4√14).

Since (x + y)^2 = x^2 + y^2 + 2xy, we have:

x^2 = (15 + 4√14)

y^2 = (15 - 4√14)

and

2xy is

2√(15 + 4√14) x √(15 - 4√14)

2√[(15 + 4√14)(15 - 4√14)]

Since (15 + 4√14)(15 - 4√14) can be written as a difference of squares, we have:

2√[(15^2) - (4√14)^2]

2√[225 - 224] = 2

Thus, the total value is:

(15 + 4√14) + (15 - 4√14) + 2 = 32

Answer: E

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