Question 1022235
If the problem is {{{(4*sqrt(400))/(4*sqrt(5))}}}, then...


<table border=1 cellpadding = 5>
<th>Step</th><th>Expression</th>
<tr><td>1.</td><td>{{{(4*sqrt(400))/(4*sqrt(5))}}}</td></tr>
<tr><td>2.</td><td>{{{(highlight(4)*sqrt(400))/(highlight(4)*sqrt(5))}}}</td></tr>
<tr><td>3.</td><td>{{{(cross(4)*sqrt(400))/(cross(4)*sqrt(5))}}}</td></tr>
<tr><td>4.</td><td>{{{(sqrt(400))/(sqrt(5))}}}</td></tr>
<tr><td>5.</td><td>{{{sqrt(400/5)}}}</td></tr>
<tr><td>6.</td><td>{{{sqrt(80)}}}</td></tr>
<tr><td>7.</td><td>{{{sqrt(16*5)}}}</td></tr>
<tr><td>8.</td><td>{{{sqrt(16)*sqrt(5)}}}</td></tr>
<tr><td>9.</td><td>{{{4*sqrt(5)}}}</td></tr>
</table>


So in the end, the expression simplifies to {{{4*sqrt(5)}}}


In other words, {{{(4*sqrt(400))/(4*sqrt(5))=4*sqrt(5)}}}


<table border = 3 bordercolor=red>
<tr><td>Final Answer: {{{4*sqrt(5)}}}</td></tr>
</table>



Notes:


* In step 5, I used the property {{{(sqrt(x))/(sqrt(y)) = sqrt(x/y)}}}


* Once I get to step 6, everything after this step is simplifying the radical. To do this, we factor 80 into 16*5 (step 7). Notice how 16 is the largest perfect square factor of 80


* In step 8, I then used {{{sqrt(x)*sqrt(y) = sqrt(x*y)}}}


* As you can see in step 9, the square root of 16 is 4 which is a whole number. This is why 80 was factored into 16*5


* Keep in mind this answer only applies if my assumption at the top is true. The assumption that the problem was {{{(4*sqrt(400))/(4*sqrt(5))}}}. If the assumption at the top is not true, then maybe the next assumption is true.


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OR


If the problem is {{{(root(4,400))/(root(4,5))}}}, then...



<table border=1 cellpadding = 5>
<th>Step</th><th>Expression</th>
<tr><td>1.</td><td>{{{(root(4,400))/(root(4,5))}}}</td></tr>
<tr><td>2.</td><td>{{{root(4,400/5)}}}</td></tr>
<tr><td>3.</td><td>{{{root(4,80)}}}</td></tr>
<tr><td>4.</td><td>{{{root(4,16*5)}}}</td></tr>
<tr><td>5.</td><td>{{{root(4,16)*root(4,5)}}}</td></tr>
<tr><td>6.</td><td>{{{2*root(4,5)}}}</td></tr>
</table>



<table border = 3 bordercolor=red>
<tr><td>Final Answer: {{{2*root(4,5)}}}</td></tr>
</table>



Notes: 


* For step 2, I used the property {{{(root(n,x))/(root(n,y)) = root(n,x/y)}}}


* For step 5, I used the property {{{root(n,x)*root(n,y) = root(n,x*y)}}}


* Like before, to simplify the fourth root of 80, I factored 80 into 16*5 because 16 is a perfect fourth root number. Taking the fourth root of 16 yields 2 (seen on step 6)


* Keep in mind this answer only applies if my assumption at the top is true. The assumption that the problem was {{{(root(4,400))/(root(4,5))}}}. If the second assumption isn't true, then go back to the first assumption (hopefully it's true. If not, then let me know)