- #1

- 19

- 0

can anyone show me how to solve this:

[tex]\sqrt{x^3} + \sqrt{1+x^3}[/tex]

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. any help is appreciated.

- Thread starter jessawells
- Start date

- #1

- 19

- 0

can anyone show me how to solve this:

[tex]\sqrt{x^3} + \sqrt{1+x^3}[/tex]

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. any help is appreciated.

- #2

- 789

- 4

Usually when you say solve an equation, you mean something like solve x + 1 = 2.

Did you mean solve :[tex]\sqrt{x^3} = \sqrt{1+x^3}[/tex] (Probably not, since this is a false statement)

or simplify

[tex]\sqrt{x^3} + \sqrt{1+x^3}[/tex]

?

I'm guessing the second one. Do you have an idea of how to approach it?

Did you mean solve :[tex]\sqrt{x^3} = \sqrt{1+x^3}[/tex] (Probably not, since this is a false statement)

or simplify

[tex]\sqrt{x^3} + \sqrt{1+x^3}[/tex]

?

I'm guessing the second one. Do you have an idea of how to approach it?

Last edited:

- #3

- 19

- 0

yes, its the second case - simplifying the expression. i'm not sure at all how to approach it. i've thought about using the fact that both terms are squared - eg. making it [tex]\sqrt{x^3 + (1+x^3)}[/tex] but i know that's wrong. other than that, i've been trying to expand the [tex]\sqrt{1+x^3}[/tex] term, the way you would expand something like [tex](1+x)^2[/tex], but i've had no success. any help would be great.

- #4

Zurtex

Science Advisor

Homework Helper

- 1,120

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Well Mathematica can't simplify it.

- #5

- 789

- 4

Agreed. That polynomial is in simplest form.

- #6

- 998

- 0

it's not a polynomial, either.

- #7

- 789

- 4

Thank you for giving us the correct definition of a polynomial.

Last edited:

- #8

- 998

- 0

[tex]\alpha_0 + \alpha_1x + \alpha_2x^2 + \ . \ . \ . \ + \alpha_nx^n.[/tex]

which [itex]\sqrt{x^3} + \sqrt{x^3+1}[/itex] certainly is not.

Now, you can certainly do some interesting things to [itex]\sqrt{x^3} + \sqrt{x^3 + 1}[/itex], as usual. For example,

[tex] \sqrt{x^3} + \sqrt{x^3 + 1} = \frac{1}{\sqrt{x^3+1}-\sqrt{x^3}}[/tex]

[tex] = \sqrt{2\sqrt{x^3}\left(\sqrt{x^3}+\sqrt{1+x^3}\right) + 1}[/tex]

but I would by no means consider those simpler.

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