Question 165407
{{{sqrt(5^99x^87y^64)}}}
<pre><font size = 4 color = "indigo"><b>
The index of a square root is 2, so we write:

{{{root(2,5^99x^87y^64)}}}

Divide the index into each exponent.

Divide index 2 into the first exponent 99
  
 <u> 49</u>
2)99
  <u>98</u>
   1 

49 is the quotient, so we will have {{{5^49}}} on
the outside in front of the radical.

1 is the remainder, so we will have {{{5^1}}} left
under the radical.  So far we have this:

{{{5^49}}}{{{root(2,5^1x^87y^64)}}}

 ---

Divide index 2 into the second exponent 87
  
 <u> 43</u>
2)87
  <u>86</u>
   1 

43 is the quotient, so we will have {{{x^43}}} on
the outside in front of the radical.

1 is the remainder, so we will have {{{x^1}}} left
under the radical.  So far we have this:

{{{5^49*x^43}}}{{{root(2,5^1x^1y^64)}}}

 ---

Divide index 2 into the third exponent 64
  
 <u> 32</u>
2)64
  <u>64</u>
   0 

32 is the quotient, so we will have {{{y^32}}} on
the outside in front of the radical.

0 is the remainder, so we will have no y's left
under the radical.  So we have:

{{{5^49*x^43*y^32}}}{{{root(2,5^1x^1)}}}

But of course when the root is a square root,
we do not write the index, so we will drop the
index 2, and the 1 exponents as well:

{{{5^49*x^43*y^32*sqrt(5x)}}}

Edwin</pre>