How does sqrt{x^[18] + x^[10]} equal (x^5)*sqrt{x^8 + 1} ?

Hello, and welcome to FMH! :)

What you have is an expression, not an equation. ;)

[MATH]\sqrt{x^{18}+x^{10}}=\sqrt{x^{10}\left(x^{8}+1\right)}=x^5\sqrt{x^{8}+1}[/MATH]
Does that make sense?
 
Hint: \(\displaystyle x^{18} = x^{10} \cdot x^8\), so \(\displaystyle x^{18} + x^{10} = x^{10}(x^8 + 1)\).
 
Thank you. I also need help with the following 2 questions.

? Moderator Note: Two images removed; reposted as separate threads.
 
In the post #1 question, where did you use "x is a positive number"?
 
It's probably best to post additional questions in new threads. Also, please show YOUR work,
 
Thank you I will do that! I’m just trying to learn how to solve these types of questions so I will know how to do them on an upcoming exam.
 
Sorry just seen the question. Im not positive where X is used as a positive Integer. I’m still not certain on how a problem like this is done.
 
blakebranham5 said:
Sorry just seen the question. Im not positive where X is used as a positive Integer. I’m still not certain on how a problem like this is done.
Click to expand...

If we don't know the sign of \(x\), then we must write:

[MATH]\sqrt{x^{2n}}=\left|x^n\right|[/MATH]
For example:

[MATH]\sqrt{(-1)^2}\ne-1[/MATH]
Instead, we must write:

[MATH]\sqrt{(-1)^2}=|-1|=1[/MATH]
So, in the given problem, knowing that \(x\) is positive, allows us to write:

[MATH]\sqrt{x^{10}}=x^5[/MATH]
 
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