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

blakebranham5

New member
Joined
Mar 4, 2019
Messages
6
How does this equation equal E?

11253
 

MarkFL

Super Moderator
Staff member
Joined
Nov 24, 2012
Messages
1,256
Hello, and welcome to FMH! :)

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

\(\displaystyle \sqrt{x^{18}+x^{10}}=\sqrt{x^{10}\left(x^{8}+1\right)}=x^5\sqrt{x^{8}+1}\)

Does that make sense?
 

ksdhart2

Senior Member
Joined
Mar 25, 2016
Messages
1,039
Hint: \(\displaystyle x^{18} = x^{10} \cdot x^8\), so \(\displaystyle x^{18} + x^{10} = x^{10}(x^8 + 1)\).
 

blakebranham5

New member
Joined
Mar 4, 2019
Messages
6
Thank you. I also need help with the following 2 questions.

💥 Moderator Note: Two images removed; reposted as separate threads.
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,816
In the post #1 question, where did you use "x is a positive number"?
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,816
It's probably best to post additional questions in new threads. Also, please show YOUR work,
 

blakebranham5

New member
Joined
Mar 4, 2019
Messages
6
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.
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,816
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.
You didn't answer my question.
 

MarkFL

Super Moderator
Staff member
Joined
Nov 24, 2012
Messages
1,256
You didn't answer my question.
It's a good question too, because understand that will help a student avoid many pitfalls down the road. :)
 

blakebranham5

New member
Joined
Mar 4, 2019
Messages
6
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.
 

MarkFL

Super Moderator
Staff member
Joined
Nov 24, 2012
Messages
1,256
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.
If we don't know the sign of \(x\), then we must write:

\(\displaystyle \sqrt{x^{2n}}=\left|x^n\right|\)

For example:

\(\displaystyle \sqrt{(-1)^2}\ne-1\)

Instead, we must write:

\(\displaystyle \sqrt{(-1)^2}=|-1|=1\)

So, in the given problem, knowing that \(x\) is positive, allows us to write:

\(\displaystyle \sqrt{x^{10}}=x^5\)
 
Top