Expert: Sherman D. - 4/3/2005

Question
hi,

i was wondering if you could show me how to solve this:

x^(3/2) + (1+x^3)^(1/2)

i want to get it to so that there's only 1 term of x. but i don't know how to expand the squared root.

note that this is not an equation (eg. not "=0"); it is an expression i want to simplify

any help is appreciated.

Answer
x^(3/2) + (1 + x^3)^(1/2)
x^(3/2) + (x^3 + 1)^(1/2)
(x^(3/2) + (x^3 + 1)^(1/2))^2
(x^(3/2) + (x^3 + 1)^(1/2))*(x^(3/2) + (x^3 + 1)^(1/2))
x^3 + 2(x^(3/2) * (x^3 + 1)^(1/2)) + (x^3 + 1)
2x^3 + 2(x^(3/2) * (x^3 + 1)^(1/2)) + 1
2x^3 + 2((x^3 * (x^3 + 1))^1/2) + 1
2x^3 + 2(x^6 + x^3)^(1/2) + 1

when you write this out, it will be

(2x^3 + 2(x^6 + x^3)^(1/2) + 1)^(1/2)

You can probably go further than that, but thats about as far as i could get.