Answer:
[tex]47x^3\sqrt{5x}[/tex]
Step-by-step explanation:
The objective is to combine the terms to make one radical, so therefore we know that we will have to take a [tex]\sqrt{5}[/tex] out of the second radical [tex]\sqrt{180}[/tex].
If we divide 180 by 5, we will get 36, so now we have
[tex]\sqrt{180}=\sqrt{5}[/tex]×[tex]\sqrt{36}[/tex]
[tex]\sqrt{36}[/tex] can be simplied into just 6.
So now the expression becomes
[tex]-\sqrt{5x^7}+8x^2*6 \sqrt{5x^3}[/tex]
Then we can further simplify by moving the [tex]x^{2}[/tex] into the radical to get two common terms with [tex]\sqrt{5x^7}[/tex].
[tex]x^{2} =\sqrt{x^4}[/tex], so we now have
[tex]-\sqrt{5x^7}+ 8\sqrt{x^4} *6 \sqrt{5x^3}[/tex]
So then we can combine the two radicals to get the expression to
[tex]-\sqrt{5x^7}+48\sqrt{5x^7}[/tex]
We now see that we have two terms with a common radical, and coefficients of -1, and 48.
That allows us to simplify further to
[tex]47\sqrt{5x^7}[/tex]
Here, we can take out [tex]\sqrt{x^6}[/tex], which is [tex]x^3[/tex], and get the final simplied form to be
[tex]47x^3\sqrt{5x}[/tex]
Hope this helped.
