How to simplify sqrt(2 + sqrt 3) + sqrt(2 - sqrt 3)?

To calculate this expression, we'll have to use the
identities:

sqrt[a+(sqrtb)] = sqrt{[a+sqrt(a^2 - b)]/2} +
sqrt{[a-sqrt(a^2 - b)]/2}

sqrt[a-(sqrtb)] =
sqrt{[a+sqrt(a^2 - b)]/2} - sqrt{[a-sqrt(a^2 - b)]/2}

Let a
= 2 and b = 3

sqrt[2+(sqrt3)] = sqrt{[2+sqrt(2^2 - 3)]/2} +
sqrt{[2-sqrt(2^2 - 3)]/2}

sqrt[2+(sqrt3)] = sqrt(3/2) +
sqrt(1/2) (1)

sqrt[2-(sqrt3)] = sqrt{[2+sqrt(2^2 - 3)]/2} -
sqrt{[2-sqrt(2^2 - 3)]/2}

sqrt[2+(sqrt3)] = sqrt(3/2) -
sqrt(1/2) (2)

We'll add (1) and (2) and we'll
get:

sqrt[2+(sqrt3)] + sqrt[2-(sqrt3)] = sqrt(3/2) +
sqrt(1/2) + sqrt(3/2) - sqrt(1/2)

We'll eliminate like
terms:

sqrt[2+(sqrt3)] + sqrt[2-(sqrt3)] =
2*sqrt(3/2)

The requested result of the
expression is sqrt[2+(sqrt3)] + sqrt[2-(sqrt3)] =
2*sqrt(3/2).